Introduction To Harmonic Analysis And Generalized Gelfand Pairs

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Introduction to Harmonic Analysis and Generalized Gelfand Pairs

Author : Gerrit van Dijk
Publisher : Walter de Gruyter
ISBN 13 : 3110220202
Total Pages : 234 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Introduction to Harmonic Analysis and Generalized Gelfand Pairs by : Gerrit van Dijk

Download or read book Introduction to Harmonic Analysis and Generalized Gelfand Pairs written by Gerrit van Dijk and published by Walter de Gruyter. This book was released on 2009-12-23 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Introduction to Harmonic Analysis and Generalized Gelfand Pairs

Author : Gerrit van Dijk
Publisher : Walter de Gruyter
ISBN 13 : 3110220199
Total Pages : 234 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Introduction to Harmonic Analysis and Generalized Gelfand Pairs by : Gerrit van Dijk

Download or read book Introduction to Harmonic Analysis and Generalized Gelfand Pairs written by Gerrit van Dijk and published by Walter de Gruyter. This book was released on 2009 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Gelfand Triples and Their Hecke Algebras

Author : Tullio Ceccherini-Silberstein
Publisher : Springer Nature
ISBN 13 : 3030516075
Total Pages : 153 pages
Book Rating : 4.0/5 (35 download)

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Book Synopsis Gelfand Triples and Their Hecke Algebras by : Tullio Ceccherini-Silberstein

Download or read book Gelfand Triples and Their Hecke Algebras written by Tullio Ceccherini-Silberstein and published by Springer Nature. This book was released on 2020-09-25 with total page 153 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences

Author : Rupert Lasser
Publisher : World Scientific
ISBN 13 : 9811266212
Total Pages : 621 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences by : Rupert Lasser

Download or read book Harmonic Analysis On Hypergroups: Approximation And Stochastic Sequences written by Rupert Lasser and published by World Scientific. This book was released on 2022-12-06 with total page 621 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Real and Functional Analysis

Author : Vladimir I. Bogachev
Publisher : Springer Nature
ISBN 13 : 3030382192
Total Pages : 586 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Real and Functional Analysis by : Vladimir I. Bogachev

Download or read book Real and Functional Analysis written by Vladimir I. Bogachev and published by Springer Nature. This book was released on 2020-02-25 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Abstract Harmonic Analysis

Author : Lynn H. Loomis
Publisher : Courier Corporation
ISBN 13 : 0486282317
Total Pages : 208 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis Introduction to Abstract Harmonic Analysis by : Lynn H. Loomis

Download or read book Introduction to Abstract Harmonic Analysis written by Lynn H. Loomis and published by Courier Corporation. This book was released on 2013-05-09 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a prominent figure in the field of harmonic analysis, this classic monograph is geared toward advanced undergraduates and graduate students and focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition.

Excursions in Harmonic Analysis, Volume 1

Author : Travis D Andrews
Publisher : Springer Science & Business Media
ISBN 13 : 0817683763
Total Pages : 489 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Excursions in Harmonic Analysis, Volume 1 by : Travis D Andrews

Download or read book Excursions in Harmonic Analysis, Volume 1 written by Travis D Andrews and published by Springer Science & Business Media. This book was released on 2013-01-04 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Analysis and Applications

Author : Michael Ruzhansky
Publisher : John Wiley & Sons
ISBN 13 : 1119414334
Total Pages : 1050 pages
Book Rating : 4.1/5 (194 download)

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Book Synopsis Mathematical Analysis and Applications by : Michael Ruzhansky

Download or read book Mathematical Analysis and Applications written by Michael Ruzhansky and published by John Wiley & Sons. This book was released on 2018-04-11 with total page 1050 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Reflection Positivity

Author : Karl-Hermann Neeb
Publisher : Springer
ISBN 13 : 3319947559
Total Pages : 139 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Reflection Positivity by : Karl-Hermann Neeb

Download or read book Reflection Positivity written by Karl-Hermann Neeb and published by Springer. This book was released on 2018-06-28 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: Refection Positivity is a central theme at the crossroads of Lie group representations, euclidean and abstract harmonic analysis, constructive quantum field theory, and stochastic processes. This book provides the first presentation of the representation theoretic aspects of Refection Positivity and discusses its connections to those different fields on a level suitable for doctoral students and researchers in related fields. It starts with a general introduction to the ideas and methods involving refection positive Hilbert spaces and the Osterwalder--Schrader transform. It then turns to Reflection Positivity in Lie group representations. Already the case of one-dimensional groups is extremely rich. For the real line it connects naturally with Lax--Phillips scattering theory and for the circle group it provides a new perspective on the Kubo--Martin--Schwinger (KMS) condition for states of operator algebras. For Lie groups Reflection Positivity connects unitary representations of a symmetric Lie group with unitary representations of its Cartan dual Lie group. A typical example is the duality between the Euclidean group E(n) and the Poincare group P(n) of special relativity. It discusses in particular the curved context of the duality between spheres and hyperbolic spaces. Further it presents some new integration techniques for representations of Lie algebras by unbounded operators which are needed for the passage to the dual group. Positive definite functions, kernels and distributions and used throughout as a central tool.

Harmonic Analysis on Commutative Spaces

Author : Joseph Albert Wolf
Publisher : American Mathematical Soc.
ISBN 13 : 9780821875230
Total Pages : 416 pages
Book Rating : 4.8/5 (752 download)

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Book Synopsis Harmonic Analysis on Commutative Spaces by : Joseph Albert Wolf

Download or read book Harmonic Analysis on Commutative Spaces written by Joseph Albert Wolf and published by American Mathematical Soc.. This book was released on 2007 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book starts with the basic theory of topological groups, harmonic analysis, and unitary representations. It then concentrates on geometric structure, harmonic analysis, and unitary representation theory in commutative spaces. Those spaces form a simultaneous generalization of compact groups, locally compact abelian groups, and riemannian symmetric spaces. Their geometry and function theory is an increasingly active topic in mathematical research, and this book brings the reader up to the frontiers of that research area with the recent classifications of weakly symmetric spaces and of Gelfand pairs.

Integral Representation Theory

Author : Jaroslav Lukeš
Publisher : Walter de Gruyter
ISBN 13 : 3110203200
Total Pages : 732 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Integral Representation Theory by : Jaroslav Lukeš

Download or read book Integral Representation Theory written by Jaroslav Lukeš and published by Walter de Gruyter. This book was released on 2010 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications

Commutative Harmonic Analysis III

Author : V.P. Havin
Publisher : Springer Science & Business Media
ISBN 13 : 3642578543
Total Pages : 272 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Commutative Harmonic Analysis III by : V.P. Havin

Download or read book Commutative Harmonic Analysis III written by V.P. Havin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aimed at readers who have learned the principles of harmonic analysis, this book provides a variety of perspectives on this very important classical subject. The authors have written a truly outstanding book which distinguishes itself by its excellent expository style.

Quantum Invariants of Knots and 3-Manifolds

Author : Vladimir G. Turaev
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110435225
Total Pages : 608 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Quantum Invariants of Knots and 3-Manifolds by : Vladimir G. Turaev

Download or read book Quantum Invariants of Knots and 3-Manifolds written by Vladimir G. Turaev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-11 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups.The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space.This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents:Invariants of graphs in Euclidean 3-space and of closed 3-manifoldsFoundations of topological quantum field theoryThree-dimensional topological quantum field theoryTwo-dimensional modular functors6j-symbolsSimplicial state sums on 3-manifoldsShadows of manifolds and state sums on shadowsConstructions of modular categories

An Introduction to Harmonic Analysis

Author : Yitzhak Katznelson
Publisher : Cambridge University Press
ISBN 13 : 9780521543590
Total Pages : 342 pages
Book Rating : 4.5/5 (435 download)

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Book Synopsis An Introduction to Harmonic Analysis by : Yitzhak Katznelson

Download or read book An Introduction to Harmonic Analysis written by Yitzhak Katznelson and published by Cambridge University Press. This book was released on 2004-01-05 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher description

Generalized Wavelets and Hypergroups

Author : Khalifa Trimeche
Publisher : Routledge
ISBN 13 : 1351445790
Total Pages : 364 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Generalized Wavelets and Hypergroups by : Khalifa Trimeche

Download or read book Generalized Wavelets and Hypergroups written by Khalifa Trimeche and published by Routledge. This book was released on 2019-01-22 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelets have recently been enjoying a period of popularity and rapid growth, and the influence of wavelet methods now extends well beyond mathematics into a number of practical fields, including statistics. The theory of hypergroups can be traced back to the turn of the century, and following its formalization in the early 1970s, the area has now

Symmetries and Laplacians

Author : David Gurarie
Publisher : Courier Corporation
ISBN 13 : 0486462889
Total Pages : 466 pages
Book Rating : 4.4/5 (864 download)

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Book Synopsis Symmetries and Laplacians by : David Gurarie

Download or read book Symmetries and Laplacians written by David Gurarie and published by Courier Corporation. This book was released on 2007-12-21 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed as an introduction to harmonic analysis and group representations, this book examines concepts, ideas, results, and techniques related to symmetry groups and Laplacians. Its exposition is based largely on examples and applications of general theory, covering a wide range of topics rather than delving deeply into any particular area. Author David Gurarie, a Professor of Mathematics at Case Western Reserve University, focuses on discrete or continuous geometrical objects and structures, such as regular graphs, lattices, and symmetric Riemannian manifolds. Starting with the basics of representation theory, Professor Gurarie discusses commutative harmonic analysis, representations of compact and finite groups, Lie groups, and the Heisenberg group and semidirect products. Among numerous applications included are integrable hamiltonian systems, geodesic flows on symmetric spaces, and the spectral theory of the Hydrogen atom (Schrodinger operator with Coulomb potential) explicated by its Runge-Lenz symmetry. Three helpful appendixes include supplemental information, and the text concludes with references, a list of frequently used notations, and an index.

A Course in Abstract Harmonic Analysis

Author : Gerald B. Folland
Publisher : CRC Press
ISBN 13 : 1498727158
Total Pages : 317 pages
Book Rating : 4.4/5 (987 download)

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Book Synopsis A Course in Abstract Harmonic Analysis by : Gerald B. Folland

Download or read book A Course in Abstract Harmonic Analysis written by Gerald B. Folland and published by CRC Press. This book was released on 2016-02-03 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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