Harmonic Analysis In Phase Space

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Harmonic Analysis in Phase Space. (AM-122), Volume 122

Gerald B. Folland
Harmonic Analysis in Phase Space AM 122 Volume 122 Book PDF

Author : Gerald B. Folland
Publisher : Princeton University Press
Page : 288 pages
File Size : 42,8 Mb
Release : 2016-03-02
Category : Mathematics
ISBN : 9781400882427

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Harmonic Analysis in Phase Space. (AM-122), Volume 122 by Gerald B. Folland Pdf

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.

Harmonic Analysis in Phase Space

G. B. Folland
Harmonic Analysis in Phase Space Book PDF

Author : G. B. Folland
Publisher : Princeton University Press
Page : 292 pages
File Size : 42,6 Mb
Release : 1989-03-21
Category : Mathematics
ISBN : 0691085285

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Harmonic Analysis in Phase Space by G. B. Folland Pdf

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

Maurice A. de Gosson
Symplectic Methods in Harmonic Analysis and in Mathematical Physics Book PDF

Author : Maurice A. de Gosson
Publisher : Springer Science & Business Media
Page : 351 pages
File Size : 42,6 Mb
Release : 2011-07-30
Category : Mathematics
ISBN : 9783764399924

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Symplectic Methods in Harmonic Analysis and in Mathematical Physics by Maurice A. de Gosson Pdf

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.

Quantum Harmonic Analysis

Maurice A. de Gosson
Quantum Harmonic Analysis Book PDF

Author : Maurice A. de Gosson
Publisher : Walter de Gruyter GmbH & Co KG
Page : 247 pages
File Size : 51,8 Mb
Release : 2021-07-05
Category : Mathematics
ISBN : 9783110722901

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Quantum Harmonic Analysis by Maurice A. de Gosson Pdf

Quantum mechanics is arguably one of the most successful scientific theories ever and its applications to chemistry, optics, and information theory are innumerable. This book provides the reader with a rigorous treatment of the main mathematical tools from harmonic analysis which play an essential role in the modern formulation of quantum mechanics. This allows us at the same time to suggest some new ideas and methods, with a special focus on topics such as the Wigner phase space formalism and its applications to the theory of the density operator and its entanglement properties. This book can be used with profit by advanced undergraduate students in mathematics and physics, as well as by confirmed researchers.

Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group

Valery V. Volchkov,Vitaly V. Volchkov
Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group Book PDF

Author : Valery V. Volchkov,Vitaly V. Volchkov
Publisher : Springer
Page : 0 pages
File Size : 45,6 Mb
Release : 2011-11-30
Category : Mathematics
ISBN : 1447122836

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Harmonic Analysis of Mean Periodic Functions on Symmetric Spaces and the Heisenberg Group by Valery V. Volchkov,Vitaly V. Volchkov Pdf

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.

Lectures on Harmonic Analysis

Thomas H. Wolff
Lectures on Harmonic Analysis Book PDF

Author : Thomas H. Wolff
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 55,9 Mb
Release : 2003-09-17
Category : Mathematics
ISBN : 9780821834497

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Lectures on Harmonic Analysis by Thomas H. Wolff Pdf

This book demonstrates how harmonic analysis can provide penetrating insights into deep aspects of modern analysis. It is both an introduction to the subject as a whole and an overview of those branches of harmonic analysis that are relevant to the Kakeya conjecture. The usual background material is covered in the first few chapters: the Fourier transform, convolution, the inversion theorem, the uncertainty principle and the method of stationary phase. However, the choice of topics is highly selective, with emphasis on those frequently used in research inspired by the problems discussed in the later chapters. These include questions related to the restriction conjecture and the Kakeya conjecture, distance sets, and Fourier transforms of singular measures. These problems are diverse, but often interconnected; they all combine sophisticated Fourier analysis with intriguing links to other areas of mathematics and they continue to stimulate first-rate work. The book focuses on laying out a solid foundation for further reading and research. Technicalities are kept to a minimum, and simpler but more basic methods are often favored over the most recent methods. The clear style of the exposition and the quick progression from fundamentals to advanced topics ensures that both graduate students and research mathematicians will benefit from the book.

Quantum Mechanics on Phase Space

Franklin E. Schroeck Jr.
Quantum Mechanics on Phase Space Book PDF

Author : Franklin E. Schroeck Jr.
Publisher : Springer Science & Business Media
Page : 687 pages
File Size : 49,9 Mb
Release : 2013-06-29
Category : Science
ISBN : 9789401728300

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Quantum Mechanics on Phase Space by Franklin E. Schroeck Jr. Pdf

In this monograph, we shall present a new mathematical formulation of quantum theory, clarify a number of discrepancies within the prior formulation of quantum theory, give new applications to experiments in physics, and extend the realm of application of quantum theory well beyond physics. Here, we motivate this new formulation and sketch how it developed. Since the publication of Dirac's famous book on quantum mechanics [Dirac, 1930] and von Neumann's classic text on the mathematical foundations of quantum mechanics two years later [von Neumann, 1932], there have appeared a number of lines of development, the intent of each being to enrich quantum theory by extra polating or even modifying the original basic structure. These lines of development have seemed to go in different directions, the major directions of which are identified here: First is the introduction of group theoretical methods [Weyl, 1928; Wigner, 1931] with the natural extension to coherent state theory [Klauder and Sudarshan, 1968; Peremolov, 1971]. The call for an axiomatic approach to physics [Hilbert, 1900; Sixth Problem] led to the development of quantum logic [Mackey, 1963; Jauch, 1968; Varadarajan, 1968, 1970; Piron, 1976; Beltrametti & Cassinelli, 1981], to the creation of the operational approach [Ludwig, 1983-85, 1985; Davies, 1976] with its application to quantum communication theory [Helstrom, 1976; Holevo, 1982), and to the development of the C* approach [Emch, 1972]. An approach through stochastic differential equations ("stochastic mechanics") was developed [Nelson, 1964, 1966, 1967].

Twentieth Century Harmonic Analysis

J.S. Byrnes
Twentieth Century Harmonic Analysis Book PDF

Author : J.S. Byrnes
Publisher : Springer Science & Business Media
Page : 411 pages
File Size : 54,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401006620

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Twentieth Century Harmonic Analysis by J.S. Byrnes Pdf

Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated. The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.

Excursions in Harmonic Analysis, Volume 4

Radu Balan,Matthew Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou
Excursions in Harmonic Analysis Volume 4 Book PDF

Author : Radu Balan,Matthew Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou
Publisher : Birkhäuser
Page : 428 pages
File Size : 54,5 Mb
Release : 2015-10-20
Category : Mathematics
ISBN : 9783319201887

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Excursions in Harmonic Analysis, Volume 4 by Radu Balan,Matthew Begué,John J. Benedetto,Wojciech Czaja,Kasso A. Okoudjou Pdf

This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers and scientists in academia, industry and government, it will be an excellent reference for graduate students, researchers and professionals in pure and applied mathematics, physics and engineering. Topics covered include: Special Topics in Harmonic Analysis Applications and Algorithms in the Physical Sciences Gabor Theory RADAR and Communications: Design, Theory, and Applications The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.

Harmonic Analysis

J. Marshall Ash,Roger L. Jones
Harmonic Analysis Book PDF

Author : J. Marshall Ash,Roger L. Jones
Publisher : American Mathematical Soc.
Page : 162 pages
File Size : 41,6 Mb
Release : 2006
Category : Harmonic analysis
ISBN : 9780821839201

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Harmonic Analysis by J. Marshall Ash,Roger L. Jones Pdf

Starting in the early 1950's, Alberto Calderon, Antoni Zygmund, and their students developed a program in harmonic analysis with far-reaching consequences. The title of these proceedings reflects this broad reach. This book came out of a DePaul University conference honoring Stephen Vagi upon his retirement in 2002. Vagi was a student of Calderon in the 1960's, when Calderon and Zygmund were at their peak. Two authors, Kenig and Gatto, were students of Calderon; one, Muckenhoupt, was a student of Zygmund. Two others studied under Zygmund's student Elias Stein. The remaining authors all have close connections with the Calderon-Zygmund school of analysis. This book should interest specialists in harmonic analysis and those curious to see it applied to partial differential equations and ergodic theory. In the first article, Adam Koranyi summarizes Vagi's work. Four additional articles cover various recent developments in harmonic analysis: Eduardo Gatto studies spaces with doubling and non-doubling measures; Cora Sadosky, product spaces; Benjamin Muckenhoupt, Laguerre expansions; and Roger Jones, singular integrals. Charles Fefferman and Carlos Kenig present applications to partial differential equations and Stephen Wainger gives an application to ergodic theory. The final article records some interesting open questions from a problem session that concluded the conference.

A Course in Abstract Harmonic Analysis

Gerald B. Folland
A Course in Abstract Harmonic Analysis Book PDF

Author : Gerald B. Folland
Publisher : CRC Press
Page : 317 pages
File Size : 47,9 Mb
Release : 2016-02-03
Category : Mathematics
ISBN : 9781498727150

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A Course in Abstract Harmonic Analysis by Gerald B. Folland Pdf

A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant resul

Real Analysis: A Comprehensive Course in Analysis, Part 1

Barry Simon
Real Analysis A Comprehensive Course in Analysis Part 1 Book PDF

Author : Barry Simon
Publisher : American Mathematical Soc.
Page : 789 pages
File Size : 53,9 Mb
Release : 2015-11-02
Category : Mathematical analysis
ISBN : 9781470410995

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Real Analysis: A Comprehensive Course in Analysis, Part 1 by Barry Simon Pdf

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 1 is devoted to real analysis. From one point of view, it presents the infinitesimal calculus of the twentieth century with the ultimate integral calculus (measure theory) and the ultimate differential calculus (distribution theory). From another, it shows the triumph of abstract spaces: topological spaces, Banach and Hilbert spaces, measure spaces, Riesz spaces, Polish spaces, locally convex spaces, Fréchet spaces, Schwartz space, and spaces. Finally it is the study of big techniques, including the Fourier series and transform, dual spaces, the Baire category, fixed point theorems, probability ideas, and Hausdorff dimension. Applications include the constructions of nowhere differentiable functions, Brownian motion, space-filling curves, solutions of the moment problem, Haar measure, and equilibrium measures in potential theory.

Classical and Multilinear Harmonic Analysis

Camil Muscalu,Wilhelm Schlag
Classical and Multilinear Harmonic Analysis Book PDF

Author : Camil Muscalu,Wilhelm Schlag
Publisher : Cambridge University Press
Page : 341 pages
File Size : 43,8 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9781107031821

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Classical and Multilinear Harmonic Analysis by Camil Muscalu,Wilhelm Schlag Pdf

This contemporary graduate-level text in harmonic analysis introduces the reader to a wide array of analytical results and techniques.

Geometric and Harmonic Analysis on Homogeneous Spaces and Applications

Ali Baklouti,Takaaki Nomura
Geometric and Harmonic Analysis on Homogeneous Spaces and Applications Book PDF

Author : Ali Baklouti,Takaaki Nomura
Publisher : Springer
Page : 234 pages
File Size : 51,9 Mb
Release : 2018-02-09
Category : Mathematics
ISBN : 9783319651811

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Geometric and Harmonic Analysis on Homogeneous Spaces and Applications by Ali Baklouti,Takaaki Nomura Pdf

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 on the Heisenberg Group

Sundaram Thangavelu
Harmonic Analysis on the Heisenberg Group Book PDF

Author : Sundaram Thangavelu
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 52,5 Mb
Release : 1998-03-24
Category : Mathematics
ISBN : 0817640509

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Harmonic Analysis on the Heisenberg Group by Sundaram Thangavelu Pdf

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 Euclidian harmonic analysis.