Introduction To Harmonic Analysis And Generalized Gelfand Pairs
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Author |
: Gerrit van Dijk |
Publisher |
: Walter de Gruyter |
Total Pages |
: 234 |
Release |
: 2009-12-23 |
ISBN-10 |
: 9783110220209 |
ISBN-13 |
: 3110220202 |
Rating |
: 4/5 (09 Downloads) |
Synopsis Introduction to Harmonic Analysis and Generalized Gelfand Pairs by : Gerrit van Dijk
This book is intended as an introduction to harmonic analysis and generalized Gelfand pairs. Starting with the elementary theory of Fourier series and Fourier integrals, the author proceeds to abstract harmonic analysis on locally compact abelian groups and Gelfand pairs. Finally a more advanced theory of generalized Gelfand pairs is developed. This book is aimed at advanced undergraduates or beginning graduate students. The scope of the book is limited, with the aim of enabling students to reach a level suitable for starting PhD research. The main prerequisites for the book are elementary real, complex and functional analysis. In the later chapters, familiarity with some more advanced functional analysis is assumed, in particular with the spectral theory of (unbounded) self-adjoint operators on a Hilbert space. From the contents Fourier series Fourier integrals Locally compact groups Haar measures Harmonic analysis on locally compact abelian groups Theory and examples of Gelfand pairs Theory and examples of generalized Gelfand pairs
Author |
: Gerrit van Dijk |
Publisher |
: Walter de Gruyter |
Total Pages |
: 234 |
Release |
: 2009 |
ISBN-10 |
: 9783110220193 |
ISBN-13 |
: 3110220199 |
Rating |
: 4/5 (93 Downloads) |
Synopsis Introduction to Harmonic Analysis and Generalized Gelfand Pairs by : Gerrit van Dijk
The series is devoted to the publication of monographs and high-level textbooks in mathematics, mathematical methods and their applications. Apart from covering important areas of current interest, a major aim is to make topics of an interdisciplinary nature accessible to the non-specialist. The works in this series are addressed to advanced students and researchers in mathematics and theoretical physics. In addition, it can serve as a guide for lectures and seminars on a graduate level. The series de Gruyter Studies in Mathematics was founded ca. 30 years ago by the late Professor Heinz Bauer and Professor Peter Gabriel with the aim to establish a series of monographs and textbooks of high standard, written by scholars with an international reputation presenting current fields of research in pure and applied mathematics. While the editorial board of the Studies has changed with the years, the aspirations of the Studies are unchanged. In times of rapid growth of mathematical knowledge carefully written monographs and textbooks written by experts are needed more than ever, not least to pave the way for the next generation of mathematicians. In this sense the editorial board and the publisher of the Studies are devoted to continue the Studies as a service to the mathematical community. Please submit any book proposals to Niels Jacob.
Author |
: Tullio Ceccherini-Silberstein |
Publisher |
: Springer Nature |
Total Pages |
: 153 |
Release |
: 2020-09-25 |
ISBN-10 |
: 9783030516079 |
ISBN-13 |
: 3030516075 |
Rating |
: 4/5 (79 Downloads) |
Synopsis Gelfand Triples and Their Hecke Algebras by : Tullio Ceccherini-Silberstein
This monograph is the first comprehensive treatment of multiplicity-free induced representations of finite groups as a generalization of finite Gelfand pairs. Up to now, researchers have been somehow reluctant to face such a problem in a general situation, and only partial results were obtained in the one-dimensional case. Here, for the first time, new interesting and important results are proved. In particular, after developing a general theory (including the study of the associated Hecke algebras and the harmonic analysis of the corresponding spherical functions), two completely new highly nontrivial and significant examples (in the setting of linear groups over finite fields) are examined in full detail. The readership ranges from graduate students to experienced researchers in Representation Theory and Harmonic Analysis.
Author |
: Travis D Andrews |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 489 |
Release |
: 2013-01-04 |
ISBN-10 |
: 9780817683764 |
ISBN-13 |
: 0817683763 |
Rating |
: 4/5 (64 Downloads) |
Synopsis Excursions in Harmonic Analysis, Volume 1 by : Travis D Andrews
The Norbert Wiener Center for Harmonic Analysis and Applications provides a state-of-the-art research venue for the broad emerging area of mathematical engineering in the context of harmonic analysis. This two-volume set consists of contributions from speakers at the February Fourier Talks (FFT) from 2006-2011. The FFT are organized by the Norbert Wiener Center in the Department of Mathematics at the University of Maryland, College Park. These volumes span a large spectrum of harmonic analysis and its applications. They are divided into the following parts: Volume I · Sampling Theory · Remote Sensing · Mathematics of Data Processing · Applications of Data Processing Volume II · Measure Theory · Filtering · Operator Theory · Biomathematics Each part provides state-of-the-art results, with contributions from an impressive array of mathematicians, engineers, and scientists in academia, industry, and government. Excursions in Harmonic Analysis: The February Fourier Talks at the Norbert Wiener Center is an excellent reference for graduate students, researchers, and professionals in pure and applied mathematics, engineering, and physics.
Author |
: Rupert Lasser |
Publisher |
: World Scientific |
Total Pages |
: 621 |
Release |
: 2022-12-06 |
ISBN-10 |
: 9789811266218 |
ISBN-13 |
: 9811266212 |
Rating |
: 4/5 (18 Downloads) |
Synopsis Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences by : Rupert Lasser
The book aims at giving a monographic presentation of the abstract harmonic analysis of hypergroups, while combining it with applied topics of spectral analysis, approximation by orthogonal expansions and stochastic sequences. Hypergroups are locally compact Hausdorff spaces equipped with a convolution, an involution and a unit element. Related algebraic structures had already been studied by Frobenius around 1900. Their axiomatic characterisation in harmonic analysis was later developed in the 1970s. Hypergoups naturally emerge in seemingly different application areas as time series analysis, probability theory and theoretical physics.The book presents harmonic analysis on commutative and polynomial hypergroups as well as weakly stationary random fields and sequences thereon. For polynomial hypergroups also difference equations and stationary sequences are considered. At greater extent than in the existing literature, the book compiles a rather comprehensive list of hypergroups, in particular of polynomial hypergroups. With an eye on readers at advanced undergraduate and graduate level, the proofs are generally worked out in careful detail. The bibliography is extensive.
Author |
: Vladimir I. Bogachev |
Publisher |
: Springer Nature |
Total Pages |
: 586 |
Release |
: 2020-02-25 |
ISBN-10 |
: 9783030382193 |
ISBN-13 |
: 3030382192 |
Rating |
: 4/5 (93 Downloads) |
Synopsis Real and Functional Analysis by : Vladimir I. Bogachev
This book is based on lectures given at "Mekhmat", the Department of Mechanics and Mathematics at Moscow State University, one of the top mathematical departments worldwide, with a rich tradition of teaching functional analysis. Featuring an advanced course on real and functional analysis, the book presents not only core material traditionally included in university courses of different levels, but also a survey of the most important results of a more subtle nature, which cannot be considered basic but which are useful for applications. Further, it includes several hundred exercises of varying difficulty with tips and references. The book is intended for graduate and PhD students studying real and functional analysis as well as mathematicians and physicists whose research is related to functional analysis.
Author |
: Alessandro Figa-Talamanca |
Publisher |
: CRC Press |
Total Pages |
: 164 |
Release |
: 2020-11-26 |
ISBN-10 |
: 9781000153293 |
ISBN-13 |
: 1000153290 |
Rating |
: 4/5 (93 Downloads) |
Synopsis Harmonic Analysis on Free Groups by : Alessandro Figa-Talamanca
This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.
Author |
: Michael Ruzhansky |
Publisher |
: John Wiley & Sons |
Total Pages |
: 1021 |
Release |
: 2018-04-11 |
ISBN-10 |
: 9781119414339 |
ISBN-13 |
: 1119414334 |
Rating |
: 4/5 (39 Downloads) |
Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky
An authoritative text that presents the current problems, theories, and applications of mathematical analysis research Mathematical Analysis and Applications: Selected Topics offers the theories, methods, and applications of a variety of targeted topics including: operator theory, approximation theory, fixed point theory, stability theory, minimization problems, many-body wave scattering problems, Basel problem, Corona problem, inequalities, generalized normed spaces, variations of functions and sequences, analytic generalizations of the Catalan, Fuss, and Fuss–Catalan Numbers, asymptotically developable functions, convex functions, Gaussian processes, image analysis, and spectral analysis and spectral synthesis. The authors—a noted team of international researchers in the field— highlight the basic developments for each topic presented and explore the most recent advances made in their area of study. The text is presented in such a way that enables the reader to follow subsequent studies in a burgeoning field of research. This important text: Presents a wide-range of important topics having current research importance and interdisciplinary applications such as game theory, image processing, creation of materials with a desired refraction coefficient, etc. Contains chapters written by a group of esteemed researchers in mathematical analysis Includes problems and research questions in order to enhance understanding of the information provided Offers references that help readers advance to further study Written for researchers, graduate students, educators, and practitioners with an interest in mathematical analysis, Mathematical Analysis and Applications: Selected Topics includes the most recent research from a range of mathematical fields.
Author |
: M. Sugiura |
Publisher |
: Elsevier |
Total Pages |
: 469 |
Release |
: 1990-03-01 |
ISBN-10 |
: 9780080887593 |
ISBN-13 |
: 0080887597 |
Rating |
: 4/5 (93 Downloads) |
Synopsis Unitary Representations and Harmonic Analysis by : M. Sugiura
The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.
Author |
: Yitzhak Katznelson |
Publisher |
: Cambridge University Press |
Total Pages |
: 342 |
Release |
: 2004-01-05 |
ISBN-10 |
: 0521543592 |
ISBN-13 |
: 9780521543590 |
Rating |
: 4/5 (92 Downloads) |
Synopsis An Introduction to Harmonic Analysis by : Yitzhak Katznelson
Publisher description