Relevant bibliographies by topics / Fourier multiplier

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Fourier multiplier'

Author: Grafiati
Published: 25 January 2025

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Journal articles on the topic "Fourier multiplier"

1

Fackler, Stephan, Tuomas P. Hytönen, and Nick Lindemulder. "Weighted estimates for operator-valued Fourier multipliers." Collectanea Mathematica 71, no. 3 (December 20, 2019): 511–48. http://dx.doi.org/10.1007/s13348-019-00275-0.

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AbstractWe establish Littlewood–Paley decompositions for Muckenhoupt weights in the setting of UMD spaces. As a consequence we obtain two-weight variants of the Mikhlin multiplier theorem for operator-valued multipliers. We also show two-weight estimates for multipliers satisfying Hörmander type conditions.
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Monica, Kommalapati, Dereddy Anuradha, Syed Rasheed, and Barnala Shereesha. "VLSI implementation of Wallace Tree Multiplier using Ladner-Fischer Adder." International Journal of Intelligent Engineering and Systems 14, no. 1 (February 28, 2021): 22–31. http://dx.doi.org/10.22266/ijies2021.0228.03.

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Nowadays, most of the application depends on arithmetic designs such as an adder, multiplier, divider, etc. Among that, multipliers are very essential for designing industrial applications such as Finite Impulse Response, Fast Fourier Transform, Discrete cosine transform, etc. In the conventional methods, different kind of multipliers such as array multiplier, booth multiplier, bough Wooley multiplier, etc. are used. These existing multipliers are occupied more area to operate. In this study, Wallace Tree Multiplier (WTM) is implemented to overcome this problem. Two kinds of multipliers have designed in this research work for comparison. At first, existing WTM is designed with normal full adders and half adders. Next, proposed WTM is designed using Ladner Fischer Adder (LFA) to improve the hardware utilization and reduce the power consumption. Field Programmable Gate Array (FPGA) performances such as slice Look Up Table (LUT), Slice Register, Bonded Input-Output Bios (IOB) and power consumption are evaluated. The proposed WTM-LFA architecture occupied 374 slice LUT, 193 slice register, 59 bonded IOB, and 26.31W power. These FPGA performances are improved compared to conventional multipliers such asModified Retiming Serial Multiplier (MRSM), Digit Based Montgomery Multiplier (DBMM), and Fast Parallel Decimal Multiplier (FPDM).
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Padmanabhan, Khamalesh Kumar, Umadevi Seerengasamy, and Abraham Sudharson Ponraj. "High-Speed Grouping and Decomposition Multiplier for Binary Multiplication." Electronics 11, no. 24 (December 16, 2022): 4202. http://dx.doi.org/10.3390/electronics11244202.

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In the computation systems that are frequently utilized in Digital Signal Processing (DSP)- and Fast Fourier transform (FFT)-based applications, binary multipliers play a crucial role. Multipliers are one of the basic arithmetic components used, and they require more hardware resources and computational time. Due to this, numerous studies have been performed so as to decrease the computational time and hardware requirements. In this research study on reducing the necessary computational time, a high-speed binary multiplier known as the Grouping and Decomposition (GD) multiplieris proposed. The proposed multiplier aims to achieve competency in processing algorithms over existing multiplier architectures through a combination of the parallel grouping of partial products of the same size and the decomposition of each grouped partial-product bit, with the final summation performed using a 5:2 logic adder (5LA). The usage of parallel processing and decomposition logic reduces the number of computation steps and hence achieves a higher speed in multiplication. The front-end and physical design implementation of the proposed GD multiplier have been executed in the 180 nm technology library using the Cadence® Virtuoso and Cadence® Virtuoso Assura tools. From the front-end design of the 8 × 8 proposed GD multiplier, it was observed that the GD multiplier achieves a reduction of approximately 56% in computation time and a reduction of 53% in power–delay product when compared to existing multiplier architectures. A further reduction in the power–delay product is achieved by the physical design implementation of the proposed multiplier due to the internal routing of subsystems with the shortest-path algorithm. The proposed multiplier works better with higher-order multiplication and is suitable for high-end applications.
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Bloom, Walter R., and Zengfu Xu. "Fourier Multipliers For Local Hardy Spaces On Chébli-Trimèche Hypergroups." Canadian Journal of Mathematics 50, no. 5 (October 1, 1998): 897–928. http://dx.doi.org/10.4153/cjm-1998-047-9.

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AbstractIn this paper we consider Fourier multipliers on local Hardy spaces hp (0 < p ≤ 1) for Chébli-Trimèche hypergroups. The molecular characterization is investigated which allows us to prove a version of Hörmander’s multiplier theorem.
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Huang, Yongdong, and Fengjuan Zhu. "Characterization of matrix Fourier multipliers for A-dilation Parseval multi-wavelet frames." International Journal of Wavelets, Multiresolution and Information Processing 13, no. 06 (November 2015): 1550051. http://dx.doi.org/10.1142/s0219691315500514.

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Let [Formula: see text] be a [Formula: see text] expansive integral matrix with [Formula: see text]. This paper investigates matrix Fourier multipliers for [Formula: see text]-dilation Parseval multi-wavelet frames, which are [Formula: see text] matrices with [Formula: see text] function entries, map [Formula: see text]-dilation Parseval multi-wavelet frames of length [Formula: see text] to [Formula: see text]-dilation Parseval multi-wavelet frames of length [Formula: see text], where [Formula: see text]. We completely characterize all matrix Fourier multipliers for [Formula: see text]-dilation Parseval multi-wavelet frames and construct several numerical examples. As Fourier wavelet frame multiplier, matrix Fourier multipliers can be used to derive new [Formula: see text]-dilation Parseval multi-wavelet frames and can help us better understand the basic properties of frame theory.
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Suvarna, S., K. Rajesh, and T. Radhu. "A Modified Architecture for Radix-4 Booth Multiplier with Adaptive Hold Logic." International Journal of Students' Research in Technology & Management 4, no. 1 (March 10, 2016): 01–05. http://dx.doi.org/10.18510/ijsrtm.2016.411.

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High speed digital multipliers are most efficiently used in many applications such as Fourier transform, discrete cosine transforms, and digital filtering. The throughput of the multipliers is based on speed of the multiplier, and then the entire performance of the circuit depends on it. The pMOS transistor in negative bias cause negative bias temperature instability (NBTI), which increases the threshold voltage of the transistor and reduces the multiplier speed. Similarly, the nMOS transistor in positive bias cause positive bias temperature instability (PBTI).These effects reduce the transistor speed and the system may fail due to timing violations. So here a new multiplier was designed with novel adaptive hold logic (AHL) using Radix-4 Modified Booth Multiplier. By using Radix-4 Modified Booth Encoding (MBE), we can reduce the number of partial products by half. Modified booth multiplier helps to provide higher throughput with low power consumption. This can adjust the AHL circuit to reduce the performance degradation. The expected result will be reduce threshold voltage, increase throughput and speed and also reduce power. This modified multiplier design is coded by Verilog and simulated using Xilinx ISE 12.1 and implemented in Spartan 3E FPGA kit.
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Tharun, Kumar Reddy M., M. Bharathi, N. Padmaja, and B. Ashreetha. "A novel multiplication design based on LUT method." i-manager's Journal on Circuits and Systems 10, no. 2 (2022): 28. http://dx.doi.org/10.26634/jcir.10.2.18907.

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Every digital signal processing application performs multiplication operations. The addition and shift operations are part of multiplication operation. Many ideas have been created for computing systems with different design goals in terms of power, area, and speed. Typical architecture of these applications include digital signal processor (DSP), fast Fourier transform (FFT), and Multiply and Accumulate (MAC) unit. This paper offers a new way to increase the speed of DSP systems. This method uses four 2x2 LUT (look-up table) multipliers to demonstrate it at a 4x4 multiplier. The proposed multiplier was created using the Xilinx Vivado software and programmed in the Verilog HDL language. In addition, the delay, area, and power consumption of the proposed multiplier design differ from those of conventional multipliers. The simulation results show that, compared to typical methods, the operation consumes less power, reaching only 3.751 W compared to the conventional multiplier of 4.804 W, and shows lower latency.
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Lebedev, V., and A. Olevskiî. "Idempotents of Fourier multiplier algebra." Geometric and Functional Analysis 4, no. 5 (September 1994): 539–44. http://dx.doi.org/10.1007/bf01896407.

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Zhao, Guoping, Jiecheng Chen, and Weichao Guo. "Remarks on the Unimodular Fourier Multipliers onα-Modulation Spaces." Journal of Function Spaces 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/106267.

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We study the boundedness properties of the Fourier multiplier operatoreiμ(D)onα-modulation spacesMp,qs,α (0≤α<1)and Besov spacesBp,qs(Mp,qs,1). We improve the conditions for the boundedness of Fourier multipliers with compact supports and for the boundedness ofeiμ(D)onMp,qs,α. Ifμis a radial functionϕ(|ξ|)andϕsatisfies some size condition, we obtain the sufficient and necessary conditions for the boundedness ofeiϕ(|D|)betweenMp1,q1s1,αandMp2,q2s2,α.
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Hong, Sangjin, Suhwan Kim, and Wayne E. Stark. "Low-power Application-specific Parallel Array Multiplier Design for DSP Applications." VLSI Design 14, no. 3 (January 1, 2002): 287–98. http://dx.doi.org/10.1080/10655140290011087.

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Digital Signal Processing (DSP) often involves multiplications with a fixed set of coefficients. This paper presents a novel multiplier design methodology for performing these coefficient multiplications with very low power dissipation. Given bounds on the throughput and the quantization error of the computation, our approach scales the original coefficients to enable the partitioning of each multiplication into a collection of smaller multiplications with shorter critical paths. Significant energy savings are achieved by performing these multiplications in parallel with a scaled supply voltage. Dissipation is further reduced when conventional array multiplier is modified disabling the multiplier rows that do not affect the multiplication's outcome. We have used our methodology to design low-power parallel array multipliers for the Fast Fourier Transform (FFT). Simulation results show that our approach can result in significant up to 76% power savings over conventional array multipliers on 64-coefficient FFT computation.
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Dissertations / Theses on the topic "Fourier multiplier"

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Wang, Li-An, and Li-An Wang. "Multiplier Theorems on Anisotropic Hardy Spaces." Thesis, University of Oregon, 2012. http://hdl.handle.net/1794/12429.

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We extend the theory of singular integral operators and multiplier theorems to the setting of anisotropic Hardy spaces. We first develop the theory of singular integral operators of convolution type in the anisotropic setting and provide a molecular decomposition on Hardy spaces that will help facilitate the study of these operators. We extend two multiplier theorems, the first by Taibleson and Weiss and the second by Baernstein and Sawyer, to the anisotropic setting. Lastly, we characterize the Fourier transforms of Hardy spaces and show that all multipliers are necessarily continuous.
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Sarybekova, Lyazzat. "Some new Lizorkin multiplier theorems for Fourier series and transforms." Licentiate thesis, Luleå : Luleå University of Technology, 2009. http://pure.ltu.se/ws/fbspretrieve/2732730.

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Thabouti, Lotfi. "Estimées de Carleman L^p globales." Electronic Thesis or Diss., Bordeaux, 2024. http://www.theses.fr/2024BORD0491.

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Dans cette thèse, on étudie des inégalités de Carleman L^p pour des problèmes elliptiques et leurs applications à la quantification du prolongement unique par rapport aux perturbations du laplacien. On s'intéresse d'abord aux inégalités de Carleman L^p sur une bande de R^d (dgeq 3), notée mathcal{S}:= (0,1) imes R^{d-1}, pour le Laplacien. Grâce à la transformée de Fourier et une factorisation de l'opérateur conjugué, nous réduisons la démonstration de ces inégalités à la construction d'une paramétrice pour le problème du Laplacien avec des conditions au bord.En utilisant cette paramétrice, on redémontre d'abord des inégalités classiques de Carleman L^2 pour le Laplacien. Ensuite, en appliquant des techniques d'analyse harmonique, notamment le théorème de restriction de Fourier pour établir des résultats de continuité de type L^p-L^q , on obtient des estimations L^p - L^q sur cette paramétrice.On applique ensuite ces méthodes au cas qui nous intéresse, à savoir les inégalités de Carleman L^p pour le Laplacien défini sur Omega , un ouvert borné et régulier de R^d (dgeq 3) , avec un second membre f_2 + f_{2 *'} + div F , f_2 in L^2(Omega), , f_{2 *'} in L^{ frac{2d}{d+2}}(Omega), ,F in L^2(Omega; C^{d}), et une condition de Dirichlet g in H^{frac{1}{2}}(partial Omega) . On montre deux estimations de Carleman globales : une sur la norme H^1 de la solution et une sur sa norme L^{frac{2d}{d-2}} , en termes de normes L^2 à poids de f_2 et F , de la norme L^{frac{2d}{d+2}} de f_{2 *'} et de la norme H^{frac{1}{2}} de g . Cela nous permet, par exemple, d'obtenir une quantification du prolongement unique pour les solutions de Delta u = V u + W_1 cdotabla u + div(W_2 u) en fonction des normes de V dans L^{q_0}(Omega) , de W_1 dans L^{q_1}(Omega) et de W_2 dans L^{q_2}(Omega) pour q_0 in (d/2, infty] et q_1 et q_2 satisfaisant soit q_1, , q_2 > (3d-2)/2 et frac{1}{q_1} + frac{1}{q_2}< 4 (1-frac{1}{d})/(3d-2) , soit q_1, , q_2 > 3d/2 .Dans une troisième partie, on étudie une quantification du prolongement unique des solutions de l'équation Delta u = V u + W_1 cdotabla u + div(W_2 u) mais avec des potentiels d'ordre un plus singuliers dans la classe limite d'intégrabilité. En particulier, on considère le cas W_1 in L^{q_1} et W_2 in L^{q_2} , avec q_1>d et q_2 >d . En utilisant le lemme de T. Wolff sur les mesures euclidiennes et une version raffinée des estimations de Carleman, on obtient des résultats de quantification du prolongement unique pour les solutions u de Delta u = V u + W_1 cdotabla u + div (W_2 u) en fonction des normes des potentiels
In this thesis, we study L^p Carleman inequalities for elliptic problems and their applications to the quantification of unique continuation with respect to perturbations of the Laplacian. We first focus on L^p Carleman inequalities on a strip of R^d (dgeq 3) , denoted mathcal{S}:= (0,1) imes R^{d-1} , for the Laplacian. Using the Fourier transform and a factorisation of the conjugate operator, we reduce the proof of these inequalities to the construction of a parametrix for the Laplacian problem with boundary conditions. Utilising this parametrix, we first reprove classical L^2 Carleman inequalities for the Laplacian. Then, applying harmonic analysis techniques, particularly the Fourier restriction theorem to establish L^p-L^q type continuity results, we obtain L^p - L^q estimates for this parametrix.We then apply these methods to the case of interest, namely L^p Carleman inequalities for the Laplacian defined on Omega , a bounded and regular open subset of R^d (d geq 3) , with a right-hand side f_2 + f_{2 *'} + div F , f_2 in L^2(Omega), , f_{2 *'} in L^{ frac{2d}{d+2}}(Omega), ,F in L^2(Omega; C^{d}) , and a Dirichlet condition g in H^{frac{1}{2}}(partial Omega) . We establish two global Carleman estimates: one on the H^1 norm of the solution and another on its L^{frac{2d}{d-2}} norm, in terms of weighted L^2 norms of f_2 and F , the L^{frac{2d}{d+2}} norm of f_{2 *'} , and the H^{frac{1}{2}} norm of g . This allows us, for example, to obtain a quantification of unique continuation for solutions of Delta u = V u + W_1 cdotabla u + div(W_2 u) in terms of the norms of V in L^{q_0}(Omega) , W_1 in L^{q_1}(Omega) , and W_2 in L^{q_2}(Omega) for q_0 in (d/2, infty] and q_1 and q_2 satisfying either q_1, , q_2 > (3d-2)/2 and frac{1}{q_1} + frac{1}{q_2}< 4(1-frac{1}{d})/(3d-2) , or q_1, , q_2 > 3d/2 .In the third part, we study a quantification of unique continuation for solutions of the equation Delta u = V u + W_1 cdotabla u + div(W_2 u) but with first-order potentials that are more singular in the limit integrability class. In particular, we consider the case where W_1 in L^{q_1} and W_2 in L^{q_2} , with q_1 > d and q_2 > d . Using T. Wolff's lemma on Euclidean measures and a refined version of Carleman estimates, we obtain unique continuation quantification results for solutions u of Delta u = V u + W_1 cdotabla u + div(W_2 u) in terms of the norms of the potentials
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Akylzhanov, Rauan. "Lp-Lq Fourier multipliers on locally compact groups." Thesis, Imperial College London, 2018. http://hdl.handle.net/10044/1/60829.

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We study the Lp − Lq boundedness of both spectral and Fourier multi- pliers on general locally compact separable unimodular groups G. As a consequence of the established Fourier multiplier theorem we also derive a spectral multiplier theorem on general locally compact separable uni- modular groups. We then apply it to obtain embedding theorems as well as time-asymptotics for the Lp − Lq norms of the heat kernels for general positive unbounded invariant operators on G. We illustrate the obtained results for sub-Laplacians on compact Lie groups and on the Heisenberg group, as well as for higher order operators. With minor modificaitons, our proofs of Paley-type inequalities and Lp − Lq bounds of Fourier multipliers can be adapted to the setting of compact homogeneous manifolds.
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Johnstone, Stephen. "Theory and applications of Fourier multipliers on locally compact groups." Thesis, University of Strathclyde, 2007. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.443141.

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Hélard, Jean-François. "Modulations codées en treillis associées à un multiplex de porteuses orthogonales en présence de canaux affectés de trajets multiples." Rennes 1, 1992. http://www.theses.fr/1992REN1S117.

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Sarkar, Avranil. "Power Prediction in Large Scale Multiple Testing: A Fourier Approach." Research Showcase @ CMU, 2010. http://repository.cmu.edu/dissertations/2.

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A problem that is frequently found in large-scale multiple testing is that, in the present stage of experiment (e.g. gene microarray, functional MRI), the signals are so faint that it is impossible to attain a desired level of testing power, and one has to enroll more samples in the follow-up experiment. Suppose we are going to enlarge the sample size by a times in the follow-up experiment, where a > 1 is not necessary an integer. A problem of great interest is, given data based on the current stage of experiment, how to predict the testing power after the sample size is enlarged by a times. We consider test z-scores and model the test statistics in the current experiment as Xj ~ N(μj , 1), 1 ≤ j ≤ n. We propose a Fourier approach to predicting the testing power after n replicates. The approach produces a very accurate prediction for moderately large values of a ( a ≤ 7). Finally, we discuss potential applications of this method on real data with emphasis on gene microarray data.
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Rodríguez, López Salvador. "Transference theory between quasi-Banach function spaces with applications to the restriction of Fourier multipliers." Doctoral thesis, Universitat de Barcelona, 2008. http://hdl.handle.net/10803/2118.

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In the early 1970 fs, R. Coifman and G. Weiss, generalizing the techniques introduced by A. Calderon, developed a method for transferring abstract convolution type operators, defined on general topological groups, and their respective bounds, to the so called gtransferred operators h, which are operators defined on general measure spaces. To be specific, if G is a topological group and R_x is a representation of G on some Banach space B and K is a convolution operator on G given by

Kf= çk(x-y) f(y) dy

with k an L^1 function, the transferred operator T is defined by letting

Tf= çk(x-y) R_xf(y) dy.

Transfer methods deal with the study of the preservation of properties of K that are still valid for T, mostly focusing on the preservation of boundedness on Lebesgue spaces Lp. These methods has been applied to several problems in Mathematical Analysis, and especially to the problem of restrict Fourier multipliers to closed subgroups. These techniques have been extended by other authors as N. Asmar, E. Berkson and A. Gillespie, among many others. It is worth noting however, that these prior developments have always been focused on inequalities for operators on Lebesgue spaces Lp.

In this thesis there are developed several transference techniques for quasi-Banach spaces more general than Lebesgue spaces Lp, as Lorentz spaces Lp, q, Orlicz-Lorentz, Lorentz-Zygmund spaces as well as for weighted Lebesgue spaces Lp(w). The most significant applications are obtained in the field of restriction of Fourier multipliers for rearrangement invariant spaces and weighted Lebesgue spaces Lp(w). Specifically, we get generalizations of the results obtained by K. De Leeuw for Fourier multipliers. There are also developed similar techniques in the context of multilinear operators of convolution type, where the basic example is the bilinear Hilbert transform, as well as for modular inequalities and inequalities arising in extrapolation
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Xu, Didi. "Bandwidth extension algorithm for multiple deterministic systems /." View abstract or full-text, 2006. http://library.ust.hk/cgi/db/thesis.pl?MECH%202006%20XU.

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Kasaei, Shohreh. "Fingerprint analysis using wavelet transform with application to compression and feature extraction." Thesis, Queensland University of Technology, 1998. https://eprints.qut.edu.au/36053/7/36053_Digitised_Thesis.pdf.

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The main goal of this research is to design an efficient compression al~ gorithm for fingerprint images. The wavelet transform technique is the principal tool used to reduce interpixel redundancies and to obtain a parsimonious representation for these images. A specific fixed decomposition structure is designed to be used by the wavelet packet in order to save on the computation, transmission, and storage costs. This decomposition structure is based on analysis of information packing performance of several decompositions, two-dimensional power spectral density, effect of each frequency band on the reconstructed image, and the human visual sensitivities. This fixed structure is found to provide the "most" suitable representation for fingerprints, according to the chosen criteria. Different compression techniques are used for different subbands, based on their observed statistics. The decision is based on the effect of each subband on the reconstructed image according to the mean square criteria as well as the sensitivities in human vision. To design an efficient quantization algorithm, a precise model for distribution of the wavelet coefficients is developed. The model is based on the generalized Gaussian distribution. A least squares algorithm on a nonlinear function of the distribution model shape parameter is formulated to estimate the model parameters. A noise shaping bit allocation procedure is then used to assign the bit rate among subbands. To obtain high compression ratios, vector quantization is used. In this work, the lattice vector quantization (LVQ) is chosen because of its superior performance over other types of vector quantizers. The structure of a lattice quantizer is determined by its parameters known as truncation level and scaling factor. In lattice-based compression algorithms reported in the literature the lattice structure is commonly predetermined leading to a nonoptimized quantization approach. In this research, a new technique for determining the lattice parameters is proposed. In the lattice structure design, no assumption about the lattice parameters is made and no training and multi-quantizing is required. The design is based on minimizing the quantization distortion by adapting to the statistical characteristics of the source in each subimage. 11 Abstract Abstract Since LVQ is a multidimensional generalization of uniform quantizers, it produces minimum distortion for inputs with uniform distributions. In order to take advantage of the properties of LVQ and its fast implementation, while considering the i.i.d. nonuniform distribution of wavelet coefficients, the piecewise-uniform pyramid LVQ algorithm is proposed. The proposed algorithm quantizes almost all of source vectors without the need to project these on the lattice outermost shell, while it properly maintains a small codebook size. It also resolves the wedge region problem commonly encountered with sharply distributed random sources. These represent some of the drawbacks of the algorithm proposed by Barlaud [26). The proposed algorithm handles all types of lattices, not only the cubic lattices, as opposed to the algorithms developed by Fischer [29) and Jeong [42). Furthermore, no training and multiquantizing (to determine lattice parameters) is required, as opposed to Powell's algorithm [78). For coefficients with high-frequency content, the positive-negative mean algorithm is proposed to improve the resolution of reconstructed images. For coefficients with low-frequency content, a lossless predictive compression scheme is used to preserve the quality of reconstructed images. A method to reduce bit requirements of necessary side information is also introduced. Lossless entropy coding techniques are subsequently used to remove coding redundancy. The algorithms result in high quality reconstructed images with better compression ratios than other available algorithms. To evaluate the proposed algorithms their objective and subjective performance comparisons with other available techniques are presented. The quality of the reconstructed images is important for a reliable identification. Enhancement and feature extraction on the reconstructed images are also investigated in this research. A structural-based feature extraction algorithm is proposed in which the unique properties of fingerprint textures are used to enhance the images and improve the fidelity of their characteristic features. The ridges are extracted from enhanced grey-level foreground areas based on the local ridge dominant directions. The proposed ridge extraction algorithm, properly preserves the natural shape of grey-level ridges as well as precise locations of the features, as opposed to the ridge extraction algorithm in [81). Furthermore, it is fast and operates only on foreground regions, as opposed to the adaptive floating average thresholding process in [68). Spurious features are subsequently eliminated using the proposed post-processing scheme.
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Books on the topic "Fourier multiplier"

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Nau, Tobias. Lp-Theory of Cylindrical Boundary Value Problems: An Operator-Valued Fourier Multiplier and Functional Calculus Approach. Wiesbaden: Vieweg+Teubner Verlag, 2012.

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Kuznet︠s︡ov, D. F. Strong approximation of multiple Ito and Stratonovich stochastic integrals: Multple Fourier series approach. Saint-Peterburg: Politechnical University Publishing House, 2011.

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Zhukova, Galina, and Margarita Rushaylo. The mathematical analysis. Volume 2. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1072172.

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The aim of the tutorial is to help students to master the basic concepts and methods of the study of calculus. In volume 2 we study analytic geometry in space; differential calculus of functions of several variables; local, conditional, global extrema of functions of several variables; multiple, curvilinear and surface integrals; elements of field theory; numerical, power series, Taylor series and Maclaurin, and Fourier series; applications to the analysis and solution of applied problems. Great attention is paid to comparison of these methods, the proper choice of study design tasks, analyze complex situations that arise in the study of these branches of mathematical analysis. For self-training and quality control knowledge given test questions. For teachers, students and postgraduate students studying mathematical analysis.
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Zhukova, Galina, and Margarita Rushaylo. Mathematical analysis in examples and tasks. Part 2. ru: INFRA-M Academic Publishing LLC., 2020. http://dx.doi.org/10.12737/1072162.

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The purpose of the textbook is to help students to master basic concepts and research methods used in mathematical analysis. In part 2 of the proposed cycle of workshops on the following topics: analytic geometry in space; differential calculus of functions of several variables; local, conditional, global extrema of functions of several variables; multiple, curvilinear and surface integrals; elements of field theory; numerical, power series, Fourier series; applications to the analysis and solution of applied problems. These topics are studied in universities, usually in the second semester in the discipline "Mathematical analysis" or the course "Higher mathematics", "Mathematics". For the development of each topic the necessary theoretical and background material, reviewed a large number of examples with detailed analysis and solutions, the options for independent work. For self-training and quality control of the acquired knowledge in each section designed exercises and tasks with answers and guidance. It is recommended that teachers, students and graduate students studying advanced mathematics.
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United States. National Aeronautics and Space Administration., ed. Compression strength of composite primary structural components: Semiannual status report, performance period, May 1, 1992 to October 31, 1992. Blacksburg, Va: Aerospace and Ocean Engineering Dept., Virginia Polytechnic Institute and State University, 1992.

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United States. National Aeronautics and Space Administration., ed. Compression strength of composite primary structural components: Semiannual status report, performance period, November 1, 1992 to April 30, 1993. Blacksburg, Va: Aerospace and Ocean Engineering Dept., Virginia Polytechnic Institute and State University, 1993.

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United States. National Aeronautics and Space Administration., ed. Compression strength of composite primary structural components: Semiannual status report, performance period, May 1, 1992 to October 31, 1992. Blacksburg, Va: Aerospace and Ocean Engineering Dept., Virginia Polytechnic Institute and State University, 1992.

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United States. National Aeronautics and Space Administration., ed. Compression strength of composite primary structural components: Semiannual status report, performance period, November 1, 1992 to April 30, 1993. Blacksburg, Va: Aerospace and Ocean Engineering Dept., Virginia Polytechnic Institute and State University, 1993.

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United States. National Aeronautics and Space Administration., ed. Compression strength of composite primary structural components: Semiannual status report, performance period, May 1, 1993 to October 31, 1993. Blacksburg, Va: Aerospace and Ocean Engineering Dept., Virginia Polytechnic Institute and State University, 1993.

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United States. National Aeronautics and Space Administration., ed. Compression strength of composite primary structural components: Semiannual status report, performance period, May 1, 1993 to October 31, 1993. Blacksburg, Va: Aerospace and Ocean Engineering Dept., Virginia Polytechnic Institute and State University, 1993.

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Book chapters on the topic "Fourier multiplier"

1

Grafakos, Loukas. "Fractional Integrability or Differentiability and Multiplier Theorems." In Fundamentals of Fourier Analysis, 195–246. Cham: Springer International Publishing, 2024. http://dx.doi.org/10.1007/978-3-031-56500-7_5.

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Nau, Tobias. "R-boundedness and operator-valued Fourier multiplier theorems." In Lp-Theory of Cylindrical Boundary Value Problems, 25–39. Wiesbaden: Vieweg+Teubner Verlag, 2012. http://dx.doi.org/10.1007/978-3-8348-2505-6_3.

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Nursultanov, Erlan, Lyazzat Sarybekova, and Nazerke Tleukhanova. "Some New Fourier Multiplier Results of Lizorkin and Hörmander Types." In Springer Proceedings in Mathematics & Statistics, 58–82. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-67053-9_6.

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Kunstmann, Peer C., and Lutz Weis. "Maximal L p -regularity for Parabolic Equations, Fourier Multiplier Theorems and $H^\infty$ -functional Calculus." In Functional Analytic Methods for Evolution Equations, 65–311. Berlin, Heidelberg: Springer Berlin Heidelberg, 2004. http://dx.doi.org/10.1007/978-3-540-44653-8_2.

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Wong, M. W. "Fourier Multipliers." In Discrete Fourier Analysis, 33–36. Basel: Springer Basel, 2011. http://dx.doi.org/10.1007/978-3-0348-0116-4_5.

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Trigub, Roald M., and Eduard S. Bellinsky. "Fourier Multipliers." In Fourier Analysis and Approximation of Functions, 309–48. Dordrecht: Springer Netherlands, 2004. http://dx.doi.org/10.1007/978-1-4020-2876-2_7.

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Duoandikoetxea, Javier. "Littlewood-Paley theory and multipliers." In Fourier Analysis, 157–94. Providence, Rhode Island: American Mathematical Society, 2000. http://dx.doi.org/10.1090/gsm/029/08.

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Novikov, Igor, and Evgenij Semenov. "Fourier-Haar Multipliers." In Haar Series and Linear Operators, 127–31. Dordrecht: Springer Netherlands, 1997. http://dx.doi.org/10.1007/978-94-017-1726-7_12.

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Grafakos, Loukas. "Littlewood–Paley Theory and Multipliers." In Classical Fourier Analysis, 1–75. New York, NY: Springer New York, 2008. http://dx.doi.org/10.1007/978-0-387-09432-8_5.

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Grafakos, Loukas. "Littlewood–Paley Theory and Multipliers." In Classical Fourier Analysis, 419–98. New York, NY: Springer New York, 2014. http://dx.doi.org/10.1007/978-1-4939-1194-3_6.

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Conference papers on the topic "Fourier multiplier"

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Molaei, Amir Masoud, Shaoqing Hu, Rupesh Kumar, and Okan Yurduseven. "Three-dimensional near-field microwave imaging with multiple-input multiple-output coded generalized reduced dimension Fourier algorithm." In Sensors and Communication Technologies in the 1 GHz to 10 THz Band, edited by Neil A. Salmon and Wladislaw Michailow, 25. SPIE, 2024. http://dx.doi.org/10.1117/12.3033684.

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Yin, Xiang, Hao Xiao, Weiwei Cao, and Shu Chen. "An Inexact Multiplier based Area-Efficient Fast Fourier Transform Processor." In 2018 2nd International Conference on Advances in Energy, Environment and Chemical Science (AEECS 2018). Paris, France: Atlantis Press, 2018. http://dx.doi.org/10.2991/aeecs-18.2018.53.

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Hara, Kensuke, and Masahiro Watanabe. "Stability Analysis of Rectangular Plates in Incompressible Flow With Fourier Multiplier Operators." In ASME 2013 Pressure Vessels and Piping Conference. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/pvp2013-97525.

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This paper describes a development of a method which improves the computational efficiency for a linear stability analysis of a plate in an uniform incompressible and irrotational flow. We introduce the Fourier multiplier operator to formulate the fluid and plate interaction problem with the mixed boundary condition. In previous typical approaches, a singular integral equation often appears in the formulation of a pressure distribution on the plate. The computation time for solving the integral equation is one of the problem encountered in the stability analysis. Applying the Fourier multiplier operator to this system, the equation of the plate-fluid interaction problem can be formulated with a pair of the Fourier and the inverse Fourier transforms. Moreover, the integration to derive the equations of motion can be efficiently carried out by using the discrete Fourier transform.
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Zhu, Lixuan, Lixing Li, and Weiwei Shan. "Design of Approximate Complex Constant Multiplier for Fast Fourier Transform in 28nm CMOS." In 2020 IEEE International Conference on Integrated Circuits, Technologies and Applications (ICTA). IEEE, 2020. http://dx.doi.org/10.1109/icta50426.2020.9332093.

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Tanida, Jun, Wataru Watanabe, and Yoshiki Ichioka. "High Accurate Optical Analog Computing Implemented on Optical Fractal Synthesizer." In Optical Computing. Washington, D.C.: Optica Publishing Group, 1995. http://dx.doi.org/10.1364/optcomp.1995.otue6.

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In the course of exploring capabilities of optical computing, optical analog scheme is important field to be researched more actively. Optical analog computing has excellent advantages, i.e., large data capacity, large processing capability, flexibility in data representation, and so on. Various optical transforms such as conventional and fractional Fourier transforms and optical techniques including vector-matrix multiplier and matched filter are good examples of the field.
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Erskine, David J., and Jerry Edelstein. "Multiple-Delay Externally Dispersed Interferometry." In Fourier Transform Spectroscopy. Washington, D.C.: OSA, 2005. http://dx.doi.org/10.1364/fts.2005.fwd2.

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Miller, Christopher W., Michael K. Yetzbacher, and Michael J. DePrenger. "Multiple Beam Fourier Transform Spectroscopy." In Fourier Transform Spectroscopy. Washington, D.C.: OSA, 2015. http://dx.doi.org/10.1364/fts.2015.fm4a.6.

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Barducci, Alessando, Donatella Guzzi, Cinzia Lastri, Paolo Marcoionni, Vanni Nardino, and Ivan Pippi. "Fourier Transform Spectrometry: the SNR disadvantage of the multiplex architecture." In Fourier Transform Spectroscopy. Washington, D.C.: OSA, 2011. http://dx.doi.org/10.1364/fts.2011.fwa5.

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Engeln, Richard, and Gerard Meijer. "A Fourier Transform Cavity Ring Down Spectrometer." In Fourier Transform Spectroscopy. Washington, D.C.: Optica Publishing Group, 2022. http://dx.doi.org/10.1364/fts.1997.ftua.1.

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Châteauneuf, François, and Roberto Heredia-Ortiz. "Channelling Induced by Multiple Reflections Inside the Beamsplitter of a Fourier Transform Spectrometer." In Fourier Transform Spectroscopy. Washington, D.C.: OSA, 2001. http://dx.doi.org/10.1364/fts.2001.fwb4.

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Reports on the topic "Fourier multiplier"

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Olsen, Daniel, and Brenna King. PR-179-18203-R01 Experimental Evaluation of Stack Testing Methods for Accurate VOC Measurement. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), February 2020. http://dx.doi.org/10.55274/r0011654.

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Volatile organic compounds (VOCs) are defined as non-methane, non-ethane hydrocarbons and have negative environmental effects, especially in the formation of ozone that creates smog. The combination of a gas chromatograph and a flame ionization detector can be implemented to quantify VOCs in engine exhaust following EPA Method 18/25A. The Fourier Transform Infrared Spectrometer can also be used to quantify VOCs in engine exhaust gas, following EPA Method 320. In this work testing and data analysis are performed with both measurement methods on multiple analyzers utilizing different engine types, conditions, and fuel quality. The accuracy of the measurement methods and data analysis approaches are compared and evaluated.
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Badrinarayanan and Olsen. PR-179-11201-R01 Performance Evaluation of Multiple Oxidation Catalysts on a Lean Burn Natural Gas Engine. Chantilly, Virginia: Pipeline Research Council International, Inc. (PRCI), August 2012. http://dx.doi.org/10.55274/r0010772.

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Two-way catalysts or oxidation catalysts are the common after-treatment systems used on lean burn natural gas engines to reduce CO, VOCs and formaldehyde emissions. The study evaluates the performance of oxidation catalysts from commercial vendors for varying catalyst temperature and space velocity. For this study, a part of the exhaust from a Waukesha VGF-18 GL lean burn natural gas engine was flowed through a catalyst slipstream system to assess the performance of the oxidation catalysts. The slipstream is used to reduce the size of the catalysts and to allow precise control of temperature and space velocity. Analyzers used include Rosemount 5-gas emissions bench, Nicolet Fourier Transform Infra-Red spectrometer and HP 5890 Series II Gas Chromatograph. The oxidation catalysts were degreened at 1200oF (650oC) for 24 hours prior to performance testing. The reduction efficencies for the emission species varied among the oxidation catalysts tested from different vendors. Most oxidation catalysts showed over 90% maximum reduction efficiencies on CO, VOCs and formaldehyde. VOC reduction efficiency was limited by poor propane emission reduction efficiency at the catalyst temperatures tested. Saturated hydrocarbons such as propane showed low reduction efficiencies on all oxidation catalysts due to high activation energy. Variation in space velocity showed very little effect on the conversion efficiencies. Most species showed over 90% conversion efficiency during the space velocity sweep. Adding more catalyst volume may not increase the reduction efficiency of emission species. Varying cell density showed very little effect on performance of the oxidation catalysts. The friction factor correlation showed the friction factor for flow through a single channel is inversely proportional to cell density.
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Battams, Nathan. Coup d’œil sur les soins familiaux et le travail au Canada. L’Institut Vanier de la famille, 2020. http://dx.doi.org/10.61959/hcoh3346f.

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Il y a fort à parier qu’un jour ou l’autre, chacun sera appelé à fournir des soins à un proche, et probablement à en recevoir aussi. En règle générale, c’est aux membres de la famille que reviennent d’abord ces responsabilités, c’est-à-dire celles de fournir et d’encadrer les soins, et parfois aussi d’en payer la note. Les familles disposent d’une étonnante capacité d’adaptation et trouvent la plupart du temps divers moyens pour mener de front leurs multiples responsabilités, obligations et engagements sur les plans familial et professionnel. Cependant, il faut parfois beaucoup de temps, d’énergie et de ressources financières pour conjuguer les soins et le travail. À cet égard, les employeurs sont appelés à jouer un rôle important pour faciliter les choses grâce à des mesures d’adaptation et en faisant preuve d’innovation et de flexibilité. Le document intitulé Coup d’œil sur les soins familiaux et le travail au Canada s’intéresse à certains contextes familiaux et tendances qui illustrent la « réalité des soins » au pays, en soulignant l’interrelation et la corrélation entre les diverses responsabilités liées à la famille, aux soins et au travail, ainsi que les liens d’interdépendance qui les unissent.
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Clausen, Jay, Richard Hark, Russ Harmon, John Plumer, Samuel Beal, and Meghan Bishop. A comparison of handheld field chemical sensors for soil characterization with a focus on LIBS. Engineer Research and Development Center (U.S.), February 2022. http://dx.doi.org/10.21079/11681/43282.

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Commercially available handheld chemical analyzers for forensic applications have been available for over a decade. Portable systems from multiple vendors can perform X-ray fluorescence (XRF) spectroscopy, Raman spectroscopy, Fourier transform infrared(FTIR) spectroscopy, and recently laser-induced breakdown spectroscopy (LIBS). Together, we have been exploring the development and potential applications of a multisensor system consisting of XRF, Raman, and LIBS for environmental characterization with a focus on soils from military ranges. Handheld sensors offer the potential to substantially increase sample throughput through the elimination of transport of samples back to the laboratory and labor-intensive sample preparation procedures. Further, these technologies have the capability for extremely rapid analysis, on the order of tens of seconds or less. We have compared and evaluated results from the analysis of several hundred soil samples using conventional laboratory bench top inductively coupled plasma atomic emission spectroscopy (ICP-AES) for metals evaluation and high-performance liquid chromatography (HPLC) and Raman spectroscopy for detection and characterization of energetic materials against handheld XRF, LIBS, and Raman analyzers. The soil samples contained antimony, copper, lead, tungsten, and zinc as well as energetic compounds such as 2,4,6-trinitrotoluene(TNT), hexahydro-1,3,5-triazine (RDX), nitroglycerine (NG), and dinitrotoluene isomers (DNT). Precision, accuracy, and sensitivity of the handheld field sensor technologies were compared against conventional laboratory instrumentation to determine their suitability for field characterization leading to decisional outcomes.
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O’Dea, Annika, and Katherine Brodie. Analysis of beach cusp formation and evolution using high‐frequency 3D lidar scans. Engineer Research and Development Center (U.S.), August 2024. http://dx.doi.org/10.21079/11681/48781.

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Beach cusp characteristics were explored using 15 months of 3D lidar scans collected hourly at the Duck, NC, Field Research Facility. Fourier analyses performed on lidar-derived beach elevation contours generated spatial cusp spectra. Active cusp events identified from the location and magnitude of each spectrum’s peak were used to evaluate conditions during cusp formation and evolution. Cusps primarily developed during normally-incident, long-period, low-energy wave conditions with low frequency spread and reflective beach conditions. Often, however, persistent upper-beach cusps lasted days to months and dynamic lower-beach cusps evolved over individual tidal cycles. At times, beaches exhibiting multiple cusp systems reverted to a single cusp system extending the entire beach when the high-tide waterline reached the upper-beach cusps, with the location and spacing of the resulting lower-beach cusps controlled by the upper-beach cusps. This is consistent with a “morphological coupling” hypothesis that hydrodynamic-morphodynamic feedbacks between the swash and upper-beach cusps can form lower-beach cusps with a related wavelength as the tide falls. However, sometimes the high-tide waterline reaching the upper-beach cusps did not result in a unified beach state. This suggest that morphological coupling is often an important factor in controlling the development of new lowerbeach cusps but cannot initiate cusp formation in hydrodynamic conditions outside those favorable for cusp activity.
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Battams, Nathan. Les soins familiaux au Canada : une réalité et un droit. L’Institut Vanier de la famille, 2016. http://dx.doi.org/10.61959/nnvo5054f.

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Au moins une fois dans sa vie, chacun sera probablement appelé à prodiguer des soins à un proche, ou à en bénéficier. En règle générale, les membres de la famille sont les premiers à fournir et à encadrer de tels soins et, dans certains cas, à payer pour ceux-ci. Qu’il s’agisse de reconduire un frère ou une sœur à un rendez-vous médical, de préparer les repas pour un grand-parent ou encore de passer à l’école prendre un enfant qui ne se sent pas bien, s’occuper de la famille semble si naturel et englobe un si vaste éventail d’activités qu’on finit souvent par oublier qu’il s’agit de soins familiaux… Ces quelques exemples font pourtant partie de cette « réalité des soins » à laquelle nous sommes habitués. Les familles disposent d’une grande capacité d’adaptation, et les gens trouvent habituellement les moyens de mener de front leurs responsabilités, leurs engagements et leurs obligations multiples sur le plan professionnel et familial. Toutefois, puisque la plupart des aidants sont aussi sur le marché du travail à plein temps, il peut s’avérer difficile de concilier travail et prestation de soins. En vertu de la notion de « situation de famille » aux termes de la Loi canadienne sur les droits de la personne, l’employeur peut être contraint de consentir certaines mesures d’adaptation à son employé qui, ayant épuisé tous les autres recours raisonnables, serait contraint de choisir entre ses obligations professionnelles et les soins à prodiguer à un membre de sa famille. De fait, les droits de la personne assurent aux travailleurs un cadre de droits et la flexibilité nécessaire afin de conjuguer leurs obligations professionnelles et leur charge de soins.
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