Harmonic Analysis In Phase Space
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Harmonic Analysis In Phase Space Am 122 Volume 122
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Author : Gerald B. Folland
language : en
Publisher: Princeton University Press
Release Date : 2016-03-02
Harmonic Analysis In Phase Space Am 122 Volume 122 written by Gerald B. Folland and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Mathematics categories.
This book provides the first coherent account of the area of analysis that involves the Heisenberg group, quantization, the Weyl calculus, the metaplectic representation, wave packets, and related concepts. This circle of ideas comes principally from mathematical physics, partial differential equations, and Fourier analysis, and it illuminates all these subjects. The principal features of the book are as follows: a thorough treatment of the representations of the Heisenberg group, their associated integral transforms, and the metaplectic representation; an exposition of the Weyl calculus of pseudodifferential operators, with emphasis on ideas coming from harmonic analysis and physics; a discussion of wave packet transforms and their applications; and a new development of Howe's theory of the oscillator semigroup.
Symplectic Methods In Harmonic Analysis And In Mathematical Physics
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Author : Maurice A. de Gosson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-07-30
Symplectic Methods In Harmonic Analysis And In Mathematical Physics written by Maurice A. de Gosson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-07-30 with Mathematics categories.
The aim of this book is to give a rigorous and complete treatment of various topics from harmonic analysis with a strong emphasis on symplectic invariance properties, which are often ignored or underestimated in the time-frequency literature. The topics that are addressed include (but are not limited to) the theory of the Wigner transform, the uncertainty principle (from the point of view of symplectic topology), Weyl calculus and its symplectic covariance, Shubin’s global theory of pseudo-differential operators, and Feichtinger’s theory of modulation spaces. Several applications to time-frequency analysis and quantum mechanics are given, many of them concurrent with ongoing research. For instance, a non-standard pseudo-differential calculus on phase space where the main role is played by “Bopp operators” (also called “Landau operators” in the literature) is introduced and studied. This calculus is closely related to both the Landau problem and to the deformation quantization theory of Flato and Sternheimer, of which it gives a simple pseudo-differential formulation where Feichtinger’s modulation spaces are key actors. This book is primarily directed towards students or researchers in harmonic analysis (in the broad sense) and towards mathematical physicists working in quantum mechanics. It can also be read with profit by researchers in time-frequency analysis, providing a valuable complement to the existing literature on the topic. A certain familiarity with Fourier analysis (in the broad sense) and introductory functional analysis (e.g. the elementary theory of distributions) is assumed. Otherwise, the book is largely self-contained and includes an extensive list of references.
Geometric And Harmonic Analysis On Homogeneous Spaces And Applications
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Author : Ali Baklouti
language : en
Publisher: Springer
Release Date : 2018-02-09
Geometric And Harmonic Analysis On Homogeneous Spaces And Applications written by Ali Baklouti and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-09 with Mathematics categories.
This book provides the latest competing research results on non-commutative harmonic analysis on homogeneous spaces with many applications. It also includes the most recent developments on other areas of mathematics including algebra and geometry. Lie group representation theory and harmonic analysis on Lie groups and on their homogeneous spaces form a significant and important area of mathematical research. These areas are interrelated with various other mathematical fields such as number theory, algebraic geometry, differential geometry, operator algebra, partial differential equations and mathematical physics. Keeping up with the fast development of this exciting area of research, Ali Baklouti (University of Sfax) and Takaaki Nomura (Kyushu University) launched a series of seminars on the topic, the first of which took place on November 2009 in Kerkennah Islands, the second in Sousse on December 2011, and the third in Hammamet on December 2013. The last seminar, which took place December 18th to 23rd 2015 in Monastir, Tunisia, has promoted further research in all the fields where the main focus was in the area of Analysis, algebra and geometry and on topics of joint collaboration of many teams in several corners. Many experts from both countries have been involved.
Harmonic Analysis
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Author : Barry Simon
language : en
Publisher: American Mathematical Soc.
Release Date : 2015-11-02
Harmonic Analysis written by Barry Simon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-11-02 with Mathematics categories.
A Comprehensive Course in Analysis by Poincaré Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis. Part 3 returns to the themes of Part 1 by discussing pointwise limits (going beyond the usual focus on the Hardy-Littlewood maximal function by including ergodic theorems and martingale convergence), harmonic functions and potential theory, frames and wavelets, spaces (including bounded mean oscillation (BMO)) and, in the final chapter, lots of inequalities, including Sobolev spaces, Calderon-Zygmund estimates, and hypercontractive semigroups.
A Comprehensive Course In Analysis
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Author : Barry Simon
language : en
Publisher:
Release Date : 2015
A Comprehensive Course In Analysis written by Barry Simon and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Mathematical analysis categories.
A Comprehensive Course in Analysis by Poincar Prize winner Barry Simon is a five-volume set that can serve as a graduate-level analysis textbook with a lot of additional bonus information, including hundreds of problems and numerous notes that extend the text and provide important historical background. Depth and breadth of exposition make this set a valuable reference source for almost all areas of classical analysis
Classical And Multilinear Harmonic Analysis
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Author : Camil Muscalu
language : en
Publisher: Cambridge University Press
Release Date : 2013-01-31
Classical And Multilinear Harmonic Analysis written by Camil Muscalu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-31 with Mathematics categories.
This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.
Harmonic Analysis Of Mean Periodic Functions On Symmetric Spaces And The Heisenberg Group
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Author : Valery V. Volchkov
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-06-13
Harmonic Analysis Of Mean Periodic Functions On Symmetric Spaces And The Heisenberg Group written by Valery V. Volchkov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-13 with Mathematics categories.
The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years. There has been much progress in a number of problems concerning local - pects of spectral analysis and spectral synthesis on homogeneous spaces. The study oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic analysis, complex analysis, partial differential equations, integral geometry, appr- imation theory, and other branches of contemporary mathematics. The present book describes recent advances in this direction of research. Symmetric spaces and the Heisenberg group are an active ?eld of investigation at 2 the moment. The simplest examples of symmetric spaces, the classical 2-sphere S 2 and the hyperbolic plane H , play familiar roles in many areas in mathematics. The n Heisenberg groupH is a principal model for nilpotent groups, and results obtained n forH may suggest results that hold more generally for this important class of Lie groups. The purpose of this book is to develop harmonic analysis of mean periodic functions on the above spaces.
Harmonic Analysis On The Heisenberg Group
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Author : Sundaram Thangavelu
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Harmonic Analysis On The Heisenberg Group written by Sundaram Thangavelu and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
The Heisenberg group plays an important role in several branches of mathematics, such as representation theory, partial differential equations, number theory, several complex variables and quantum mechanics. This monograph deals with various aspects of harmonic analysis on the Heisenberg group, which is the most commutative among the non-commutative Lie groups, and hence gives the greatest opportunity for generalizing the remarkable results of Euclidean harmonic analysis. The aim of this text is to demonstrate how the standard results of abelian harmonic analysis take shape in the non-abelian setup of the Heisenberg group. Thangavelu’s exposition is clear and well developed, and leads to several problems worthy of further consideration. Any reader who is interested in pursuing research on the Heisenberg group will find this unique and self-contained text invaluable.
Harmonic Analysis And Partial Differential Equations
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Author : Justin Feuto
language : en
Publisher: Springer Nature
Release Date : 2024-09-12
Harmonic Analysis And Partial Differential Equations written by Justin Feuto and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-09-12 with Mathematics categories.
This proceedings volume collects selected papers presented at the Harmonic Analysis and Applications Workshop held in Abidjan, Côte d'Ivoire from May 22-26, 2023. Chapters present surveys and recent research results from experts and cover a range of topics at the intersections of classical and abstract harmonic analysis, PDEs, and numerical analysis.
Classical And Multilinear Harmonic Analysis Volume 2
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Author : Camil Muscalu
language : en
Publisher: Cambridge University Press
Release Date : 2013-01-31
Classical And Multilinear Harmonic Analysis Volume 2 written by Camil Muscalu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-31 with Mathematics categories.
This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and useful to graduates and researchers in pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. The first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.