Thematische Bibliographien / Fourier and Schur multipliers

Auswahl der wissenschaftlichen Literatur zum Thema „Fourier and Schur multipliers“

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Veröffentlicht am 7. Juli 2024

Zuletzt aktualisiert am 7. Juli 2024

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Zeitschriftenartikel zum Thema "Fourier and Schur multipliers"

Arhancet, Cédric. „Unconditionality, Fourier multipliers and Schur multipliers“. Colloquium Mathematicum 127, Nr. 1 (2012): 17–37. http://dx.doi.org/10.4064/cm127-1-2.

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Neuwirth, Stefan, und Éric Ricard. „Transfer of Fourier Multipliers into Schur Multipliers and Sumsets in a Discrete Group“. Canadian Journal of Mathematics 63, Nr. 5 (18.10.2011): 1161–87. http://dx.doi.org/10.4153/cjm-2011-053-9.

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Abstract We inspect the relationship between relative Fourier multipliers on noncommutative Lebesgue– Orlicz spaces of a discrete group and relative Toeplitz-Schur multipliers on Schatten–von- Neumann–Orlicz classes. Four applications are given: lacunary sets, unconditional Schauder bases for the subspace of a Lebesgue space determined by a given spectrum , the norm of the Hilbert transformand the Riesz projection on Schatten–von-Neumann classes with exponent a power of 2, and the norm of Toeplitz Schur multipliers on Schatten–von-Neumann classes with exponent less than 1.

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Olevskii, Victor. „A connection between Fourier and Schur multipliers“. Integral Equations and Operator Theory 25, Nr. 4 (Dezember 1996): 496–500. http://dx.doi.org/10.1007/bf01203030.

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Spronk, Nico. „Measurable schur multipliers and completely bounded multipliers of the Fourier algebras“. Proceedings of the London Mathematical Society 89, Nr. 01 (30.06.2004): 161–92. http://dx.doi.org/10.1112/s0024611504014650.

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HAAGERUP, U., T. STEENSTRUP und R. SZWARC. „SCHUR MULTIPLIERS AND SPHERICAL FUNCTIONS ON HOMOGENEOUS TREES“. International Journal of Mathematics 21, Nr. 10 (Oktober 2010): 1337–82. http://dx.doi.org/10.1142/s0129167x10006537.

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Let X be a homogeneous tree of degree q + 1 (2 ≤ q ≤ ∞) and let ψ : X × X → ℂ be a function for which ψ(x, y) only depends on the distance between x, y ∈ X. Our main result gives a necessary and sufficient condition for such a function to be a Schur multiplier on X × X. Moreover, we find a closed expression for the Schur norm ||ψ||S of ψ. As applications, we obtaina closed expression for the completely bounded Fourier multiplier norm ||⋅||M0A(G) of the radial functions on the free (non-abelian) group 𝔽N on N generators (2 ≤ N ≤ ∞) and of the spherical functions on the q-adic group PGL2(ℚq) for every prime number q.

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ANOUSSIS, M., A. KATAVOLOS und I. G. TODOROV. „Ideals of the Fourier algebra, supports and harmonic operators“. Mathematical Proceedings of the Cambridge Philosophical Society 161, Nr. 2 (02.05.2016): 223–35. http://dx.doi.org/10.1017/s0305004116000256.

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AbstractWe examine the common null spaces of families of Herz–Schur multipliers and apply our results to study jointly harmonic operators and their relation with jointly harmonic functionals. We show how an annihilation formula obtained in [1] can be used to give a short proof as well as a generalisation of a result of Neufang and Runde concerning harmonic operators with respect to a normalised positive definite function. We compare the two notions of support of an operator that have been studied in the literature and show how one can be expressed in terms of the other.

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Harcharras, Asma. „Fourier analysis, Schur multipliers on $S^p$ and non-commutative Λ(p)-sets“. Studia Mathematica 137, Nr. 3 (1999): 203–60. http://dx.doi.org/10.4064/sm-137-3-203-260.

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Caspers, Martijn, und Mikael de la Salle. „Schur and Fourier multipliers of an amenable group acting on non-commutative $L^p$-spaces“. Transactions of the American Mathematical Society 367, Nr. 10 (04.03.2015): 6997–7013. http://dx.doi.org/10.1090/s0002-9947-2015-06281-3.

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Caspers, Martijn, und Gerrit Vos. „BMO spaces of $\sigma $-finite von Neumann algebras and Fourier–Schur multipliers on ${\rm SU}_q(2)$“. Studia Mathematica 262, Nr. 1 (2022): 45–91. http://dx.doi.org/10.4064/sm201202-18-6.

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Hladnik, Milan. „Compact Schur multipliers“. Proceedings of the American Mathematical Society 128, Nr. 9 (28.02.2000): 2585–91. http://dx.doi.org/10.1090/s0002-9939-00-05708-7.

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Dissertationen zum Thema "Fourier and Schur multipliers"

Zeng, Kai. „Some problems in harmonic analysis on twsited crossed products“. Electronic Thesis or Diss., Bourgogne Franche-Comté, 2023. http://www.theses.fr/2023UBFCD048.

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Cette thèse a pour but d’étudier quelques problèmes dans l'analyse harmonique sur les produits croisés tordus qui sont définis par des actions tordues d'un groupe localement compact G sur une algèbre de von Neumann M. Elle se compose de deux parties. La première porte sur les produits croisés tordus et leurs multiplicateurs de Fourier et de Schur. Nous démontrons que la propriété d’être QWEP pour l’algèbre de von Neumann tordue d’un groupe G est indépendante du 2-cocycle sous-ajacent et que les Lp-multiplicateurs de Fourier complètement bornés sur cette algèbre tordue sont aussi indépendants du 2-cocycle. Sous l’hypothèse d’une action moyennable, nous établissons plusieurs résultats de transfert entre les multiplicateurs de Fourier et de Schur sur les espaces Lp non-commutatifs du produit croisé tordu.Dans la deuxième partie, nous étudions les commutateurs de multiplicateurs de Fourier sur le produit croisé tordu d’un espace euclidien. Nous caractérisons leur appartenance à la p-classes de Schatten par celle de leurs symboles à un espace de Besov associé. Cette partie contient aussi une formule sur la trace de Dixmier qui nous donne également une caractérisation de l’appartenance de ces commutateurs à une p-classe de Schatten faible par un espace de Sobolev. En particulier, nos résultats s'appliquent au cas d’un espace euclidien quantique
This thesis is devoted to the study of some problems in the harmonic analysis on twisted crossed products defined by twisted actions of a locally compact group G on a von Neumann algebra M. It consists of two parts. The first concerns twisted crossed products and their Fourier and Schur multipliers. We prove that the property of being QWEP for the twisted von Neumann algebra of a group G is independent of the underlying 2-cocycle and that the completely bounded Lp-Fourier multipliers on this twisted algebra are also independent of the 2-cocycle. Under the hypothesis of an amenable action, we establish several transference results between the Fourier and Schur multipliers on the noncommutative Lp spaces of the twisted crossed product.In the second part, we study Fourier multiplier commutators on the twisted crossed product of an Euclidean space. We characterize their Schatten p-class membership by that of their symbols in the associated Besov space. In addition, this part contains a formula on the Dixmier trace, which also gives us a characterization of the weak Schatten p-class membership of these commutators by a Sobolev space. In particular, our results apply to the case of quantum Euclidean spaces

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McKee, Andrew. „Multipliers of dynamical systems“. Thesis, Queen's University Belfast, 2017. https://pure.qub.ac.uk/portal/en/theses/multipliers-of-dynamical-systems(65b93a06-6e7b-420b-ae75-c28d373f8bdf).html.

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Herz–Schur multipliers of a locally compact group have a well developed theory coming from a large literature; they have proved very useful in the study of the reduced C∗-algebra of a locally compact group. There is also a rich connection to Schur multipliers,which have been studied since the early twentieth century, and have a large number of applications. We develop a theory of Herz–Schur multipliers of a C∗-dynamical system, extending the classical Herz–Schur multipliers, making Herz–Schur multiplier techniques available to study a much larger class of C∗-algebras. Furthermore, we will also introduce and study generalised Schur multipliers, and derive links between these two notions which extend the classical results describing Herz–Schur multipliers in terms of Schur multipliers. This theory will be developed in as much generality as possible, with reference to the classical motivation. After introducing all the necessary concepts we begin the investigation by defining generalised Schur multipliers. The main result is a dilation type characterisation of these multipliers; we also show how such multipliers can be represented using HilbertC∗-modules. Next we introduce and study generalised Herz–Schur multipliers, first extending a classical result involving the representation theory of SU(2), before studying how such functions are related to our generalised Schur multipliers. We give a characterisation of generalised Herz–Schur multipliers as a certain class of the generalised Schur multipliers, and obtain a description of precisely which Schur multipliers belong to this class. Finally, we consider some ways in which the generalised multipliers can arise; firstly, from the classical multipliers which provide our motivation, secondly, from the Haagerup tensor product of a C∗-algebra with itself, and finally from positivity considerations. We show that our theory behaves well with respect to positivity and give conditions under which our multipliers are automatically positive in a natural sense.

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Steen, Naomi Mary. „Unbounded generalisations of Schur and operator multipliers“. Thesis, Queen's University Belfast, 2013. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.603070.

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Bounded Schur multipliers were introduced and characterised several decades ago, and various applications of this algebra of functions have been discovered. More recently, research into different classes of unbounded multipliers has been carried out. In this thesis the theory of one such class, that of the local Schur multipliers, is extended in different settings. A dilation of minimal Stinespring representations of completely positive, bimodular maps on spaces of compact operators is obtained, and used to establish an unbounded version of Stinespring's Theorem. This theorem is applied to obtain a characterisation of positive local Schur multipliers. In addition, a relation is demonstrated between operator monotone functions and positive local Schur multipliers, and a description is given of positive multipliers of Toeplitz type. The theory of local multipliers is extended to the multidimensional setting, and a characterisation of such functions is obtained. Local operator multipliers are introduced as a non-commutative e analogue of local Schur multipliers and a description is provided, extending previously known results concerning completely bounded operator multipliers. Positive multipliers are defined in this setting) and characterised using elements of canonical positive cones. The two-dimensional Fourier algebra A2(G) of a compact, abelian group G is considered, and a number of results are obtained concerning the Arens product on its dual, VN(G) ®uh VN(G). It is shown that A2 (G) may be viewed as a left VN(G) ®ub VN(G)-module, and thus certain results of Eyroard are extended to the two-dimensional setting, leading to the establishment of a condition equivalent to the homeomorphic identification of the Gelfand spectrum of A2(G) with C2 .

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Coine, Clément. „Continuous linear and bilinear Schur multipliers and applications to perturbation theory“. Thesis, Bourgogne Franche-Comté, 2017. http://www.theses.fr/2017UBFCD074/document.

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Dans le premier chapitre, nous commençons par définir certains produits tensoriels et identifions leur dual. Nous donnons ensuite quelques propriétés des classes de Schatten. La fin du chapitre est dédiée à l’étude des espaces de Bochner à valeurs dans l'espace des opérateurs factorisables par un espace de Hilbert. Le deuxième chapitre est consacré aux multiplicateurs de Schur linéaires. Nous caractérisons les multiplicateurs bornés sur B(Lp, Lq) lorsque p est inférieur à q puis appliquons ce résultat pour obtenir de nouvelles relations d'inclusion entre espaces de multiplicateurs. Dans le troisième chapitre, nous caractérisons, au moyen de multiplicateurs de Schur linéaires, les multiplicateurs de Schur bilinéaires continus à valeurs dans l'espace des opérateurs à trace. Dans le quatrième chapitre, nous donnons divers résultats concernant les opérateurs intégraux multiples. En particulier, nous caractérisons les opérateurs intégraux triples à valeurs dans l'espace des opérateurs à trace puis nous donnons une condition nécessaire et suffisante pour qu'un opérateur intégral triple définisse une application complètement bornée sur le produit de Haagerup de l'espace des opérateurs compacts. Enfin, le cinquième chapitre est dédié à la résolution des problèmes de Peller. Nous commençons par étudier le lien entre opérateurs intégraux multiples et théorie de la perturbation pour le calcul fonctionnel des opérateurs autoadjoints pour finir par la construction de contre-exemples à ces problèmes
In the first chapter, we define some tensor products and we identify their dual space. Then, we give some properties of Schatten classes. The end of the chapter is dedicated to the study of Bochner spaces valued in the space of operators that can be factorized by a Hilbert space.The second chapter is dedicated to linear Schur multipliers. We characterize bounded multipliers on B(Lp, Lq) when p is less than q and then apply this result to obtain new inclusion relationships among spaces of multipliers.In the third chapter, we characterize, by means of linear Schur multipliers, continuous bilinear Schur multipliers valued in the space of trace class operators. In the fourth chapter, we give several results concerning multiple operator integrals. In particular, we characterize triple operator integrals mapping valued in trace class operators and then we give a necessary and sufficient condition for a triple operator integral to define a completely bounded map on the Haagerup tensor product of compact operators. Finally, the fifth chapter is dedicated to the resolution of Peller's problems. We first study the connection between multiple operator integrals and perturbation theory for functional calculus of selfadjoint operators and we finish with the construction of counter-examples for those problems

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Marcoci, Liviu-Gabriel. „A study of Schur multipliers and some Banach spaces of infinite matrices : /“. Luleå : Department of Mathematics, Luleå University of Technology, 2010. http://pure.ltu.se/ws/fbspretrieve/4554227.

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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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Mathias, Maximilian [Verfasser], E. [Gutachter] Schmidt und J. [Gutachter] Schur. „Über positive Fourier-Integrale / Maximilian Mathias ; Gutachter: E. Schmidt, J. Schur“. Berlin : Humboldt-Universität zu Berlin, 2006. http://d-nb.info/1206192313/34.

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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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Marcoci, Liviu-Gabriel. „Some new results concerning Schur multipliers and duality results between Bergman-Schatten and little Bloch spaces /“. Luleå : Luleå University of Technology, 2009. http://pure.ltu.se/ws/fbspretrieve/2732750.

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Marcoci, Anca-Nicoleta. „Some new results concerning Lorentz sequence spaces and Schur multipliers : characterization of some new Banach spaces of infinite matrices“. Licentiate thesis, Luleå : Luleå University of Technology, 2009. http://pure.ltu.se/ws/fbspretrieve/2727437.

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Bücher zum Thema "Fourier and Schur multipliers"

United States. National Aeronautics and Space Administration., Hrsg. 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., Hrsg. 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., Hrsg. 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., Hrsg. 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., Hrsg. Compression strength of composite primary structural components: Semiannual status report : performance period: May 1, 1994 to October 31, 1994. Blacksburg, Va: Aerospace and Ocean Engineering Dept., Virginia Polytechnic and State University, 1994.

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United States. National Aeronautics and Space Administration., Hrsg. 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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Popa, Nicolae, und Lars Erik Persson. Matrix Spaces and Schur Multipliers: Matriceal Harmonic Analysis. World Scientific Publishing Co Pte Ltd, 2014.

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Trebels, W. Multipliers for (C,alpha)-Bounded Fourier Expansions in Banach Spaces and Approximation Theory. Springer London, Limited, 2006.

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R-Boundedness, Fourier Multipliers, and Problems of Elliptic and Parabolic Type (Memoirs of the American Mathematical Society). American Mathematical Society, 2003.

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Buchteile zum Thema "Fourier and Schur multipliers"

Pisier, Gilles. „Hankelian Schur multipliers. Herz-Schur multipliers“. In Lecture Notes in Mathematics, 107–15. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-662-21537-1_7.

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Pisier, Gilles. „6. Hankelian Schur multipliers. Herz-Schur multipliers“. In Lecture Notes in Mathematics, 114–23. Berlin, Heidelberg: Springer Berlin Heidelberg, 2001. http://dx.doi.org/10.1007/978-3-540-44563-0_7.

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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., und 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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Novikov, Igor, und 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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Pisier, Gilles. „Schur multipliers and Grothendieck’s inequality“. In Lecture Notes in Mathematics, 92–106. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/978-3-662-21537-1_6.

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Dym, Harry, und Dan Volok. „Pick Matrices for Schur Multipliers“. In Characteristic Functions, Scattering Functions and Transfer Functions, 133–38. Basel: Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-0346-0183-2_6.

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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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Hieber, Matthias. „Operator Valued Fourier Multipliers“. In Topics in Nonlinear Analysis, 363–80. Basel: Birkhäuser Basel, 1999. http://dx.doi.org/10.1007/978-3-0348-8765-6_17.

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Edmunds, David E., Vakhtang Kokilashvili und Alexander Meskhi. „Multipliers of Fourier Transforms“. In Bounded and Compact Integral Operators, 593–615. Dordrecht: Springer Netherlands, 2002. http://dx.doi.org/10.1007/978-94-015-9922-1_9.

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Konferenzberichte zum Thema "Fourier and Schur multipliers"

Masri, Rohaidah, Hazzirah Izzati Mat Hassim, Nor Haniza Sarmin, Nor Muhainiah Mohd Ali und Nor'ashiqin Mohd Idrus. „The generalization of the Schur multipliers of Bieberbach groups“. In INTERNATIONAL CONFERENCE ON QUANTITATIVE SCIENCES AND ITS APPLICATIONS (ICOQSIA 2014): Proceedings of the 3rd International Conference on Quantitative Sciences and Its Applications. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4903622.

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Mat Hassim, Hazzirah Izzati, Nor Haniza Sarmin, Nor Muhainiah Mohd Ali, Rohaidah Masri und Nor'ashiqin Mohd Idrus. „The Schur multipliers of certain Bieberbach groups with abelian point groups“. In PROCEEDINGS OF THE 20TH NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES: Research in Mathematical Sciences: A Catalyst for Creativity and Innovation. AIP, 2013. http://dx.doi.org/10.1063/1.4801248.

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Ydyrys, Aizhan Zh, und Nazerke T. Tleukhanova. „On multipliers of Fourier series in the Lorentz space“. In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2016). Author(s), 2016. http://dx.doi.org/10.1063/1.4959739.

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Toft, Joachim. „Pseudo-Differential Operators, Fourier Multipliers and Non-stationary Filters on Modulation Spaces“. In MATHEMATICAL MODELING OF WAVE PHENOMENA: 2nd Conference on Mathematical Modeling of Wave Phenomena. AIP, 2006. http://dx.doi.org/10.1063/1.2205819.

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Lee, Kyung Chul, Hyesuk Chae, Shiqi Xu, Kyungwon Lee, Roarke Horstmeyer, Byung-Woo Hong und Seung Ah Lee. „Fourier Ptychographic Iterative Engine Based on Alternating Direction Method of Multipliers with Anisotropic Total-Variation Regularization“. In Computational Optical Sensing and Imaging. Washington, D.C.: Optica Publishing Group, 2023. http://dx.doi.org/10.1364/cosi.2023.cm4b.4.

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We propose an ADMM-based phase retrieval algorithm for FP that utilizes anisotropic total variation regularization for the object function and L2 regularization for pupil functions. All our results in simulation and real experiments demonstrate that our algorithm outperforms the Gauss-Newton algorithm in terms of object and pupil function recovery. Our findings suggest that our algorithm enables the reconstruction of the objective function using a shorter exposure time and fewer measurements as a factor of 60x.

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Chen, Qingjiang, Bingzhe Wei und Yanbo Zhang. „On Matrix Fourier Multipliers for Semi-orthonormal Binary Framelets and Perturbation of Gabor Frames and Applications“. In 3rd International Conference on Mechatronics, Robotics and Automation. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/icmra-15.2015.276.

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Geng, Yu, Li Chen, Heng Liu, Shemiao Qi, Yi Liu, Rui Zhou, Rongfeng Zhang, Bowen Fan, Yinsi Chen und Yuan Li. „Numerical Methods for Improving the Optimization Efficiency of Textured Surfaces“. In ASME 2023 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2023. http://dx.doi.org/10.1115/imece2023-111458.

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Abstract As an emerging tribological technology, surface texturing has been widely studied and applied. More and more scholars have committed to the theoretical optimization of textures. To improve the optimization efficiency of textured surfaces, a multiscale method combining the finite cell method with Fischer-Burmeister-Newton-Schur, named as FCM-FBNS, the Fourier Amplitude Sensitivity Test (FAST) and genetic algorithm (GA) were combined in this paper. The proposed methods can calculate the first-order sensitivity indices of texturing parameters to the tribological characteristics efficiently and fastly. Results show that the texture density is the most crucial geometric parameter; the effects of the cell size are negligible. In addition, the effects of texturing parameters have a close relationship with operating conditions and the same parameters may have different influences on different static characteristics. The parameters with higher sensitivity indices can be defined as the key ones and the GA method was applied to improve the tribological performance of textured surfaces by optimizing these texturing parameters. The results achieved by optimizing only the key parameters are similar to that of optimizing all parameters, but the time can be saving up to 30 percent. The methods not only can reduce the optimization difficulty and time, but also provide a novel perspective to understand the optimization problem by quantifing the influence of input on the output.

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Bajkova, A. T., und B. Roy Frieden. „Maximum entropy restoration of ISAR images.“ In OSA Annual Meeting. Washington, D.C.: Optica Publishing Group, 1992. http://dx.doi.org/10.1364/oam.1992.thqq8.

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ISAR (interactive synthetic aperture radar) images are formed by Fourier transformation of complex frequency-space data. These generally suffer from noise and can also be degraded by under-sampling due to deliberate frequency skipping. Such a problem of incomplete information is typically well handled by the concept of maximum entropy. However, to apply the approach one has to force maximum entropy in a complex function. This was accomplished as follows (ATB). Each part (real or imaginary) is regarded as the difference between two associated, positive-only functions. The latter are forced to not overlap, through the action of a tuning parameter. Then the overall entropy is the sum of the ordinary entropies of the associated functions. This approach was adapted (BRF) into a MAP estimation algorithm where the entropy steps are absorbed into a prior probability law and the likelihood law allows for Gaussian noise. Because the exp(·) imaging kernel is separable in x and y,the 2-D processing problem can be implemented as a sequence of 1-D problems, first row-wise and then column-wise. An ordinary Newton-Raphson procedure solves for the unknown Lagrange multipliers defining each 1-D problem. ISAR image examples will be shown.

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