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Relevant bibliographies by topics / Analytic Hilbert Spaces

Academic literature on the topic 'Analytic Hilbert Spaces'

Author: Grafiati

Published: 6 September 2023

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Journal articles on the topic "Analytic Hilbert Spaces"

1

de Branges, Louis. "Nodal Hilbert spaces of analytic functions." Journal of Mathematical Analysis and Applications 108, no. 2 (June 1985): 447–65. http://dx.doi.org/10.1016/0022-247x(85)90038-1.

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Wang, Kai. "Analytic Extension of Functions from Analytic Hilbert Spaces*." Chinese Annals of Mathematics, Series B 28, no. 3 (April 30, 2007): 321–26. http://dx.doi.org/10.1007/s11401-005-0526-9.

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Upmeier, Harald. "Hilbert modules and complex analytic fibre spaces." Rendiconti Lincei - Matematica e Applicazioni 32, no. 3 (December 16, 2021): 565–91. http://dx.doi.org/10.4171/rlm/949.

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Chen, Xiaoman, Kunyu Guo, and Shengzhao Hou. "Analytic Hilbert Spaces over the Complex Plane." Journal of Mathematical Analysis and Applications 268, no. 2 (April 2002): 684–700. http://dx.doi.org/10.1006/jmaa.2001.7839.

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Burtnyak, I., I. Chernega, V. Hladkyi, O. Labachuk, and Z. Novosad. "Application of symmetric analytic functions to spectra of linear operators." Carpathian Mathematical Publications 13, no. 3 (December 11, 2021): 701–10. http://dx.doi.org/10.15330/cmp.13.3.701-710.

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The paper is devoted to extension of the theory of symmetric analytic functions on Banach sequence spaces to the spaces of nuclear and $p$-nuclear operators on the Hilbert space. We introduced algebras of symmetric polynomials and analytic functions on spaces of $p$-nuclear operators, described algebraic bases of such algebras and found some connection with the Fredholm determinant of a nuclear operator. In addition, we considered cases of compact and bounded normal operators on the Hilbert space and discussed structures of symmetric polynomials on corresponding spaces.

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Chen, Qiuhui, Luoqing Li, and Weibin Wu. "Amplitude spaces of mono-components from Blaschke products and an intrinsic multiresolution analysis." International Journal of Wavelets, Multiresolution and Information Processing 18, no. 06 (September 15, 2020): 2050051. http://dx.doi.org/10.1142/s0219691320500514.

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A mono-component is a real-variable and complex-valued analytic signal with nonnegative frequency components. The amplitude of an analytic signal is determined by its phase in a canonical amplitude-phase modulation. This paper investigates the amplitude spaces of analytic signals in terms of the Blaschke products with zeros in [Formula: see text]. It is proved that these amplitude spaces are invariant under the Hilbert transform and form a multiresolution analysis in the Hilbert space of signals with finite energy.

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Hou, Shengzhao, and Shuyun Wei. "Ordered analytic Hilbert spaces over the unit disk." Studia Mathematica 185, no. 2 (2008): 127–42. http://dx.doi.org/10.4064/sm185-2-2.

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Lanucha, Bartosz, Maria Nowak, and Miroslav Pavlovic. "Hilbert matrix operator on spaces of analytic functions." Annales Academiae Scientiarum Fennicae Mathematica 37 (February 2012): 161–74. http://dx.doi.org/10.5186/aasfm.2012.3715.

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Yousefi, B. "Multiplication operators on Hilbert spaces of analytic functions." Archiv der Mathematik 83, no. 6 (December 2004): 536–39. http://dx.doi.org/10.1007/s00013-004-1040-0.

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Guo, Kunyu. "Characteristic Spaces and Rigidity for Analytic Hilbert Modules." Journal of Functional Analysis 163, no. 1 (April 1999): 133–51. http://dx.doi.org/10.1006/jfan.1998.3380.

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Dissertations / Theses on the topic "Analytic Hilbert Spaces"

1

Ameur, Yacin. "Interpolation of Hilbert spaces /." Uppsala : Matematiska institutionen, Univ. [distributör], 2001. http://publications.uu.se/theses/91-506-1531-9/.

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Harris, Terri Joan Mrs. "HILBERT SPACES AND FOURIER SERIES." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/244.

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I give an overview of the basic theory of Hilbert spaces necessary to understand the convergence of the Fourier series for square integrable functions. I state the necessary theorems and definitions to understand the formulations of the problem in a Hilbert space framework, and then I give some applications of the theory along the way.

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Lapinski, Felicia. "Hilbert spaces and the Spectral theorem." Thesis, Uppsala universitet, Analys och sannolikhetsteori, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-454412.

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Sorensen, Julian Karl. "White noise analysis and stochastic evolution equations." Title page, contents and abstract only, 2001. http://web4.library.adelaide.edu.au/theses/09PH/09phs713.pdf.

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Tipton, James Edward. "Reproducing Kernel Hilbert spaces and complex dynamics." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2284.

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Both complex dynamics and the theory of reproducing kernel Hilbert spaces have found widespread application over the last few decades. Although complex dynamics started over a century ago, the gravity of it's importance was only recently realized due to B.B. Mandelbrot's work in the 1980's. B.B. Mandelbrot demonstrated to the world that fractals, which are chaotic patterns containing a high degree of self-similarity, often times serve as better models to nature than conventional smooth models. The theory of reproducing kernel Hilbert spaces also having started over a century ago, didn't pick up until N. Aronszajn's classic was written in 1950. Since then, the theory has found widespread application to fields including machine learning, quantum mechanics, and harmonic analysis. In the paper, Infinite Product Representations of Kernel Functions and Iterated Function Systems, the authors, D. Alpay, P. Jorgensen, I. Lewkowicz, and I. Martiziano, show how a kernel function can be constructed on an attracting set of an iterated function system. Furthermore, they show that when certain conditions are met, one can construct an orthonormal basis of the associated Hilbert space via certain pull-back and multiplier operators. In this thesis we take for our iterated function system, the family of iterates of a given rational map. Thus we investigate for which rational maps their kernel construction holds as well as their orthornormal basis construction. We are able to show that the kernel construction applies to any rational map conjugate to a polynomial with an attracting fixed point at 0. Within such rational maps, we are able to find a family of polynomials for which the orthonormal basis construction holds. It is then natural to ask how the orthonormal basis changes as the polynomial within a given family varies. We are able to determine for certain families of polynomials, that the dynamics of the corresponding orthonormal basis is well behaved. Finally, we conclude with some possible avenues of future investigation.

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Giulini, Ilaria. "Generalization bounds for random samples in Hilbert spaces." Thesis, Paris, Ecole normale supérieure, 2015. http://www.theses.fr/2015ENSU0026/document.

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Ce travail de thèse porte sur l'obtention de bornes de généralisation pour des échantillons statistiques à valeur dans des espaces de Hilbert définis par des noyaux reproduisants. L'approche consiste à obtenir des bornes non asymptotiques indépendantes de la dimension dans des espaces de dimension finie, en utilisant des inégalités PAC-Bayesiennes liées à une perturbation Gaussienne du paramètre et à les étendre ensuite aux espaces de Hilbert séparables. On se pose dans un premier temps la question de l'estimation de l'opérateur de Gram à partir d'un échantillon i. i. d. par un estimateur robuste et on propose des bornes uniformes, sous des hypothèses faibles de moments. Ces résultats permettent de caractériser l'analyse en composantes principales indépendamment de la dimension et d'en proposer des variantes robustes. On propose ensuite un nouvel algorithme de clustering spectral. Au lieu de ne garder que la projection sur les premiers vecteurs propres, on calcule une itérée du Laplacian normalisé. Cette itération, justifiée par l'analyse du clustering en termes de chaînes de Markov, opère comme une version régularisée de la projection sur les premiers vecteurs propres et permet d'obtenir un algorithme dans lequel le nombre de clusters est déterminé automatiquement. On présente des bornes non asymptotiques concernant la convergence de cet algorithme, lorsque les points à classer forment un échantillon i. i. d. d'une loi à support compact dans un espace de Hilbert. Ces bornes sont déduites des bornes obtenues pour l'estimation d'un opérateur de Gram dans un espace de Hilbert. On termine par un aperçu de l'intérêt du clustering spectral dans le cadre de l'analyse d'images
This thesis focuses on obtaining generalization bounds for random samples in reproducing kernel Hilbert spaces. The approach consists in first obtaining non-asymptotic dimension-free bounds in finite-dimensional spaces using some PAC-Bayesian inequalities related to Gaussian perturbations and then in generalizing the results in a separable Hilbert space. We first investigate the question of estimating the Gram operator by a robust estimator from an i. i. d. sample and we present uniform bounds that hold under weak moment assumptions. These results allow us to qualify principal component analysis independently of the dimension of the ambient space and to propose stable versions of it. In the last part of the thesis we present a new algorithm for spectral clustering. It consists in replacing the projection on the eigenvectors associated with the largest eigenvalues of the Laplacian matrix by a power of the normalized Laplacian. This iteration, justified by the analysis of clustering in terms of Markov chains, performs a smooth truncation. We prove nonasymptotic bounds for the convergence of our spectral clustering algorithm applied to a random sample of points in a Hilbert space that are deduced from the bounds for the Gram operator in a Hilbert space. Experiments are done in the context of image analysis

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Awunganyi, John. "A study of optimization in Hilbert Space." CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/1459.

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Zandler, Andersson Nils. "Boundedness of a Class of Hilbert Operators on Modulation Spaces." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-84932.

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In this work we take interest in frames and modulation spaces. On the basis of their properties, we show how frame expansions can be used to prove the boundedness of a particular class of Hilbert operators on modulation spaces taking advantage of the special category of piece-wise polynomial functions known as B-splines.

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Leon, Ralph Daniel. "Module structure of a Hilbert space." CSUSB ScholarWorks, 2003. https://scholarworks.lib.csusb.edu/etd-project/2469.

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This paper demonstrates the properties of a Hilbert structure. In order to have a Hilbert structure it is necessary to satisfy certain properties or axioms. The main body of the paper is centered on six questions that develop these ideas.

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Agora, Elona. "Boundedness of the Hilbert Transform on Weighted Lorentz Spaces." Doctoral thesis, Universitat de Barcelona, 2012. http://hdl.handle.net/10803/108930.

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The main goal of this thesis is to characterize the weak-type (resp. strong-type) boundedness of the Hilbert transform H on weighted Lorentz spaces Λpu(w). The characterization is given in terms of some geometric conditions on the weights u and w and the weak-type (resp. strong-type) boundedness of the Hardy-Littlewood maximal operator on the same spaces. Our results extend and unify simultaneously the theory of the boundedness of H on weighted Lebesgue spaces Lp(u) and Muckenhoupt weights Ap, and the theory on classical Lorentz spaces Λp(w) and Ariño-Muckenhoupt weights Bp.
Títol: Acotaciò de l'operador de Hilbert sobre espais de Lorentz amb pesos Resum: L'objectiu principal d'aquesta tesi es caracteritzar l'acotació de l'operador de Hilbert sobre els espais de Lorentz amb pesos Λpu(w). També estudiem la versió dèbil. La caracterització es dona en terminis de condicions geomètriques sobre els pesos u i w, i l'acotació de l'operador maximal de Hardy-Littlewood sobre els mateixos espais. Els nostres resultats unifiquen dues teories conegudes i aparentment no relacionades entre elles, que tracten l'acotació de l'operador de Hilbert sobre els espais de Lebegue amb pesos Lp(u) per una banda i els espais de Lorentz clàssics Λp(w) per altre banda.

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Books on the topic "Analytic Hilbert Spaces"

1

Mashreghi, Javad. Hilbert spaces of analytic functions. Providence, R.I: American Mathematical Society, 2010.

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Mashreghi, Javad. Hilbert spaces of analytic functions. Providence, R.I: American Mathematical Society, 2010.

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3

Javad, Mashreghi, Ransford Thomas, and Seip Kristian 1962-, eds. Hilbert spaces of analytic functions. Providence, R.I: American Mathematical Society, 2010.

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Vakhtang, Paatashvili, ed. Boundary value problems for analytic and harmonic functions in nonstandard Banach function spaces. Hauppauge, N.Y: Nova Science Publishers, 2011.

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Ilʹi︠a︡shenko, I︠U︡ S. Lectures on analytic differential equations. Providence, R.I: American Mathematical Society, 2008.

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Mashreghi, Javad, Emmanuel Fricain, and William T. Ross. Invariant subspaces of the shift operator: CRM Workshop, Invariant Subspaces of the Shift Operator, August 26-30, 2013, Centre de Recherches Mathematiques, Universite' de Montreal, Montreal. Providence, Rhode Island: American Mathematical Society, 2015.

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7

Plymen, Roger J. Spinors in Hilbert space. Cambridge [England]: Cambridge University Press, 1994.

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8

Kesavan, S. Functional analysis. New Delhi: Hindustan Book Agency, 2009.

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Zaidman, Samuel. Functional analysis and differential equations in abstract spaces. Boca Raton, Fla: Chapman & Hall/CRC, 1999.

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10

Steeb, W. H. Hilbert spaces, generalized functions and quantum mechanics. Mannheim: BI-Wissenschaftsverlag, 1991.

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Book chapters on the topic "Analytic Hilbert Spaces"

1

Post, Olaf. "The Functional Analytic Part: Two Operators in Different Hilbert Spaces." In Lecture Notes in Mathematics, 187–257. Berlin, Heidelberg: Springer Berlin Heidelberg, 2012. http://dx.doi.org/10.1007/978-3-642-23840-6_4.

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2

Post, Olaf. "The Functional Analytic Part: Scales of Hilbert Spaces and Boundary Triples." In Lecture Notes in Mathematics, 97–185. Berlin, Heidelberg: Springer Berlin Heidelberg, 2011. http://dx.doi.org/10.1007/978-3-642-23840-6_3.

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Babbitt, Donald. "Certain Hilbert Spaces of Analytic Functions Associated With the Heisenberg Group." In Studies in Mathematical Physics: Essays in Honor of Valentine Bargmann, edited by Elliott H. Lieb, 19–82. Princeton: Princeton University Press, 2015. http://dx.doi.org/10.1515/9781400868940-004.

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D’Angelo, John P. "Hilbert Spaces." In Hermitian Analysis, 45–94. New York, NY: Springer New York, 2013. http://dx.doi.org/10.1007/978-1-4614-8526-1_2.

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Kesavan, S. "Hilbert Spaces." In Functional Analysis, 195–230. Gurgaon: Hindustan Book Agency, 2009. http://dx.doi.org/10.1007/978-93-86279-42-2_7.

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Loeb, Peter A. "Hilbert Spaces." In Real Analysis, 127–45. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-30744-2_8.

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Muscat, Joseph. "Hilbert Spaces." In Functional Analysis, 171–219. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-06728-5_10.

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8

Krall, Allan M. "Hilbert Spaces." In Applied Analysis, 127–57. Dordrecht: Springer Netherlands, 1986. http://dx.doi.org/10.1007/978-94-009-4748-1_7.

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D’Angelo, John P. "Hilbert spaces." In Hermitian Analysis, 43–92. Cham: Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-16514-7_2.

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10

Pedersen, Gert K. "Hilbert Spaces." In Analysis Now, 79–125. New York, NY: Springer New York, 1989. http://dx.doi.org/10.1007/978-1-4612-1007-8_3.

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Conference papers on the topic "Analytic Hilbert Spaces"

1

Sridhar, M., Ch Srinivasa Rao, K. Padma Raju, and D. Venkata Ratnam. "Spectral analysis of ionospheric phase scintillations using Hilbert — Huang transform at a low-latitude GNSS station." In 2015 International Conference on Signal Processing And Communication Engineering Systems (SPACES). IEEE, 2015. http://dx.doi.org/10.1109/spaces.2015.7058204.

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Kuzenkov, Oleg A., and Vladimir A. Grishagin. "Global optimization in Hilbert space." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952195.

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Liu, Ying. "Image analysis using Hilbert space." In EI 92, edited by James R. Sullivan, Benjamin M. Dawson, and Majid Rabbani. SPIE, 1992. http://dx.doi.org/10.1117/12.58352.

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Zhu, Xiu-Ge, Xiao-Jing Zhang, and Guo-Chang Wu. "Some properties of Bessel sequences in Hilbert spaces." In 2012 International Conference on Wavelet Analysis and Pattern Recognition (ICWAPR). IEEE, 2012. http://dx.doi.org/10.1109/icwapr.2012.6294800.

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Schmidt, Torge, and Marko Lindner. "Approximation of pseudospectra on a Hilbert space." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2015 (ICNAAM 2015). Author(s), 2016. http://dx.doi.org/10.1063/1.4952286.

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Varwandkar, S. D. "Hilbert space analysis for power networks." In 2016 IEEE 6th International Conference on Power Systems (ICPS). IEEE, 2016. http://dx.doi.org/10.1109/icpes.2016.7584085.

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Stoica, Diana, and Mihail Megan. "Concepts of dichotomy for stochastic skew-evolution semiflows in Hilbert spaces." In NUMERICAL ANALYSIS AND APPLIED MATHEMATICS ICNAAM 2012: International Conference of Numerical Analysis and Applied Mathematics. AIP, 2012. http://dx.doi.org/10.1063/1.4756246.

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Paiva, Antonio R. C., Il Park, and Jose C. Principe. "Reproducing kernel Hilbert spaces for spike train analysis." In ICASSP 2008 - 2008 IEEE International Conference on Acoustics, Speech and Signal Processing. IEEE, 2008. http://dx.doi.org/10.1109/icassp.2008.4518834.

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VIERU, ALINA ILINCA. "ON THE MINIMUM ENERGY PROBLEM FOR LINEAR SYSTEMS IN HILBERT SPACES." In Applied Analysis and Differential Equations - The International Conference. WORLD SCIENTIFIC, 2007. http://dx.doi.org/10.1142/9789812708229_0029.

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Akgül, A., and M. Giyas Sakar. "A new application of reproducing kernel Hilbert space method." In INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS (ICNAAM 2017). Author(s), 2018. http://dx.doi.org/10.1063/1.5044176.

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