Fourier And Fourier Stieltjes Algebras On Locally Compact Groups

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Fourier and Fourier-Stieltjes Algebras on Locally Compact Groups

Author : Eberhard Kaniuth
Publisher : American Mathematical Soc.
ISBN 13 : 0821853651
Total Pages : 306 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fourier and Fourier-Stieltjes Algebras on Locally Compact Groups by : Eberhard Kaniuth

Download or read book Fourier and Fourier-Stieltjes Algebras on Locally Compact Groups written by Eberhard Kaniuth and published by American Mathematical Soc.. This book was released on 2018-07-05 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of the Fourier algebra lies at the crossroads of several areas of analysis. Its roots are in locally compact groups and group representations, but it requires a considerable amount of functional analysis, mainly Banach algebras. In recent years it has made a major connection to the subject of operator spaces, to the enrichment of both. In this book two leading experts provide a road map to roughly 50 years of research detailing the role that the Fourier and Fourier-Stieltjes algebras have played in not only helping to better understand the nature of locally compact groups, but also in building bridges between abstract harmonic analysis, Banach algebras, and operator algebras. All of the important topics have been included, which makes this book a comprehensive survey of the field as it currently exists. Since the book is, in part, aimed at graduate students, the authors offer complete and readable proofs of all results. The book will be well received by the community in abstract harmonic analysis and will be particularly useful for doctoral and postdoctoral mathematicians conducting research in this important and vibrant area.

Fourier Analysis on Groups

Author : Walter Rudin
Publisher : Courier Dover Publications
ISBN 13 : 0486821013
Total Pages : 304 pages
Book Rating : 4.4/5 (868 download)

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Book Synopsis Fourier Analysis on Groups by : Walter Rudin

Download or read book Fourier Analysis on Groups written by Walter Rudin and published by Courier Dover Publications. This book was released on 2017-04-19 with total page 304 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by a master mathematical expositor, this classic text reflects the results of the intense period of research and development in the area of Fourier analysis in the decade preceding its first publication in 1962. The enduringly relevant treatment is geared toward advanced undergraduate and graduate students and has served as a fundamental resource for more than five decades. The self-contained text opens with an overview of the basic theorems of Fourier analysis and the structure of locally compact Abelian groups. Subsequent chapters explore idempotent measures, homomorphisms of group algebras, measures and Fourier transforms on thin sets, functions of Fourier transforms, closed ideals in L1(G), Fourier analysis on ordered groups, and closed subalgebras of L1(G). Helpful Appendixes contain background information on topology and topological groups, Banach spaces and algebras, and measure theory.

Kac Algebras and Duality of Locally Compact Groups

Author : Michel Enock
Publisher : Springer Science & Business Media
ISBN 13 : 3662028131
Total Pages : 266 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Kac Algebras and Duality of Locally Compact Groups by : Michel Enock

Download or read book Kac Algebras and Duality of Locally Compact Groups written by Michel Enock and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the theory of Kac algebras and their dual ity, elaborated independently by M. Enock and J . -M. Schwartz, and by G. !. Kac and L. !. Vajnermann in the seventies. The sub ject has now reached a state of maturity which fully justifies the publication of this book. Also, in recent times, the topic of "quantum groups" has become very fashionable and attracted the attention of more and more mathematicians and theoret ical physicists. One is still missing a good characterization of quantum groups among Hopf algebras, similar to the character ization of Lie groups among locally compact groups. It is thus extremely valuable to develop the general theory, as this book does, with emphasis on the analytical aspects of the subject instead of the purely algebraic ones. The original motivation of M. Enock and J. -M. Schwartz can be formulated as follows: while in the Pontrjagin duality theory of locally compact abelian groups a perfect symmetry exists between a group and its dual, this is no longer true in the various duality theorems of T. Tannaka, M. G. Krein, W. F. Stinespring . . . dealing with non abelian locally compact groups. The aim is then, in the line proposed by G. !. Kac in 1961 and M. Takesaki in 1972, to find a good category of Hopf algebras, containing the category of locally compact groups and fulfilling a perfect duality.

Fourier Analysis of Unbounded Measures on Locally Compact Abelian Groups

Author : Loren N. Argabright
Publisher : American Mathematical Soc.
ISBN 13 : 0821818457
Total Pages : 61 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fourier Analysis of Unbounded Measures on Locally Compact Abelian Groups by : Loren N. Argabright

Download or read book Fourier Analysis of Unbounded Measures on Locally Compact Abelian Groups written by Loren N. Argabright and published by American Mathematical Soc.. This book was released on 1974 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: In harmonic analysis on a LCA group G, the term "Fourier transform" has a variety of meanings. It refers to various objects constructed in special ways, depending on the desired theory. The standard theories include the theory of Fourier-Stieltjes transforms, the Plancherel theorem, and the Bochner theorem can be viewed as another aspect of this phenomenon. However, except for special cases, we know of no attempt in the literature to undertake the desired synthesis. The purpose of the present work is to give a systematic account of such an attempt.

Harmonic Functions on Groups and Fourier Algebras

Author : Cho-Ho Chu
Publisher : Springer
ISBN 13 : 3540477934
Total Pages : 100 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Harmonic Functions on Groups and Fourier Algebras by : Cho-Ho Chu

Download or read book Harmonic Functions on Groups and Fourier Algebras written by Cho-Ho Chu and published by Springer. This book was released on 2004-10-11 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph introduces some new aspects to the theory of harmonic functions and related topics. The authors study the analytic algebraic structures of the space of bounded harmonic functions on locally compact groups and its non-commutative analogue, the space of harmonic functionals on Fourier algebras. Both spaces are shown to be the range of a contractive projection on a von Neumann algebra and therefore admit Jordan algebraic structures. This provides a natural setting to apply recent results from non-associative analysis, semigroups and Fourier algebras. Topics discussed include Poisson representations, Poisson spaces, quotients of Fourier algebras and the Murray-von Neumann classification of harmonic functionals.

Multipliers, Positive Functionals, Positive-Definite Functions, and Fourier-Stieltjes Transforms

Author : Kelly McKennon
Publisher : American Mathematical Soc.
ISBN 13 : 0821818112
Total Pages : 75 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Multipliers, Positive Functionals, Positive-Definite Functions, and Fourier-Stieltjes Transforms by : Kelly McKennon

Download or read book Multipliers, Positive Functionals, Positive-Definite Functions, and Fourier-Stieltjes Transforms written by Kelly McKennon and published by American Mathematical Soc.. This book was released on 1971 with total page 75 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Trends in Banach Spaces and Operator Theory

Author : Anna Kamińska
Publisher : American Mathematical Soc.
ISBN 13 : 0821832344
Total Pages : 386 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Trends in Banach Spaces and Operator Theory by : Anna Kamińska

Download or read book Trends in Banach Spaces and Operator Theory written by Anna Kamińska and published by American Mathematical Soc.. This book was released on 2003 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains proceedings of the conference on Trends in Banach Spaces and Operator Theory, which was devoted to recent advances in theories of Banach spaces and linear operators. Included in the volume are 25 papers, some of which are expository, while others present new results. The articles address the following topics: history of the famous James' theorem on reflexivity, projective tensor products, construction of noncommutative $L p$-spaces via interpolation, Banach spaces with abundance of nontrivial operators, Banach spaces with small spaces of operators, convex geometry of Coxeter-invariant polyhedra, uniqueness of unconditional bases in quasi-Banach spaces, dynamics of cohyponormal operators, and Fourier algebras for locally compact groupoids. The book is suitable for graduate students and research mathematicians interested in Banach spaces and operator theory and their applications.

Banach Algebras and Applications

Author : Mahmoud Filali
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110600439
Total Pages : 307 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Banach Algebras and Applications by : Mahmoud Filali

Download or read book Banach Algebras and Applications written by Mahmoud Filali and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-08-24 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Banach Function Algebras, Arens Regularity, and BSE Norms

Author : Harold Garth Dales
Publisher : Springer Nature
ISBN 13 : 3031445325
Total Pages : 452 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Banach Function Algebras, Arens Regularity, and BSE Norms by : Harold Garth Dales

Download or read book Banach Function Algebras, Arens Regularity, and BSE Norms written by Harold Garth Dales and published by Springer Nature. This book was released on with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Abstract Harmonic Analysis

Author : Edwin Hewitt
Publisher : Springer
ISBN 13 : 3642620086
Total Pages : 778 pages
Book Rating : 4.6/5 (426 download)

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Book Synopsis Abstract Harmonic Analysis by : Edwin Hewitt

Download or read book Abstract Harmonic Analysis written by Edwin Hewitt and published by Springer. This book was released on 2013-12-21 with total page 778 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a continuation of vol. I (Grundlehren vol. 115, also available in softcover), and contains a detailed treatment of some important parts of harmonic analysis on compact and locally compact abelian groups. From the reviews: "This work aims at giving a monographic presentation of abstract harmonic analysis, far more complete and comprehensive than any book already existing on the subject...in connection with every problem treated the book offers a many-sided outlook and leads up to most modern developments. Carefull attention is also given to the history of the subject, and there is an extensive bibliography...the reviewer believes that for many years to come this will remain the classical presentation of abstract harmonic analysis." Publicationes Mathematicae

Operator Methods in Wavelets, Tilings, and Frames

Author : Keri A. Kornelson
Publisher : American Mathematical Soc.
ISBN 13 : 1470410400
Total Pages : 177 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Operator Methods in Wavelets, Tilings, and Frames by : Keri A. Kornelson

Download or read book Operator Methods in Wavelets, Tilings, and Frames written by Keri A. Kornelson and published by American Mathematical Soc.. This book was released on 2014-10-20 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Harmonic Analysis of Frames, Wavelets, and Tilings, held April 13-14, 2013, in Boulder, Colorado. Frames were first introduced by Duffin and Schaeffer in 1952 in the context of nonharmonic Fourier series but have enjoyed widespread interest in recent years, particularly as a unifying concept. Indeed, mathematicians with backgrounds as diverse as classical and modern harmonic analysis, Banach space theory, operator algebras, and complex analysis have recently worked in frame theory. Frame theory appears in the context of wavelets, spectra and tilings, sampling theory, and more. The papers in this volume touch on a wide variety of topics, including: convex geometry, direct integral decompositions, Beurling density, operator-valued measures, and splines. These varied topics arise naturally in the study of frames in finite and infinite dimensions. In nearly all of the papers, techniques from operator theory serve as crucial tools to solving problems in frame theory. This volume will be of interest not only to researchers in frame theory but also to those in approximation theory, representation theory, functional analysis, and harmonic analysis.

Banach Algebras on Semigroups and on Their Compactifications

Author : Harold G. Dales
Publisher : American Mathematical Soc.
ISBN 13 : 0821847759
Total Pages : 178 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Banach Algebras on Semigroups and on Their Compactifications by : Harold G. Dales

Download or read book Banach Algebras on Semigroups and on Their Compactifications written by Harold G. Dales and published by American Mathematical Soc.. This book was released on 2010 with total page 178 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Volume 205, number 966 (end of volume)."

Topological Vector Spaces, Algebras and Related Areas

Author : A Lau
Publisher : CRC Press
ISBN 13 : 9780582257771
Total Pages : 284 pages
Book Rating : 4.2/5 (577 download)

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Book Synopsis Topological Vector Spaces, Algebras and Related Areas by : A Lau

Download or read book Topological Vector Spaces, Algebras and Related Areas written by A Lau and published by CRC Press. This book was released on 1995-05-15 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of an international conference held to mark the retirement of Professor Taqdir Husain from McMaster University. The contributions, covering topics such as topological vector spaces, topological algebras and related areas, reflect Husain's research interests and present surveys and new research in the topics of the conference.

Banach Algebras and Their Applications

Author : Anthony To-Ming Lau
Publisher : American Mathematical Soc.
ISBN 13 : 0821834711
Total Pages : 343 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Banach Algebras and Their Applications by : Anthony To-Ming Lau

Download or read book Banach Algebras and Their Applications written by Anthony To-Ming Lau and published by American Mathematical Soc.. This book was released on 2004 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume is from the international conference on Banach algebras and their applications held at the University of Alberta (Edmonton). It contains a collection of refereed research papers and high-level expository articles that offer a panorama of Banach algebra theory and its manifold applications. Topics in the book range from $K$-theory to abstract harmonic analysis to operator theory. It is suitable for graduate students and researchers interested in Banach algebras.

Lie Algebras and Locally Compact Groups

Author : Irving Kaplansky
Publisher : University of Chicago Press
ISBN 13 : 0226424537
Total Pages : 161 pages
Book Rating : 4.2/5 (264 download)

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Book Synopsis Lie Algebras and Locally Compact Groups by : Irving Kaplansky

Download or read book Lie Algebras and Locally Compact Groups written by Irving Kaplansky and published by University of Chicago Press. This book was released on 1971 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents lecture notes based on the author's courses on Lie algebras and the solution of Hilbert's fifth problem. In chapter 1, "Lie Algebras," the structure theory of semi-simple Lie algebras in characteristic zero is presented, following the ideas of Killing and Cartan. Chapter 2, "The Structure of Locally Compact Groups," deals with the solution of Hilbert's fifth problem given by Gleason, Montgomery, and Zipplin in 1952.

Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory

Author : Robert S. Doran
Publisher : American Mathematical Soc.
ISBN 13 : 0821851276
Total Pages : 215 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory by : Robert S. Doran

Download or read book Selfadjoint and Nonselfadjoint Operator Algebras and Operator Theory written by Robert S. Doran and published by American Mathematical Soc.. This book was released on 1991 with total page 215 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers presented at the NSF/CBMS Regional Conference on Coordinates in Operator Algebras, held at Texas Christian University in Fort Worth in May 1990. During the conference, in addition to a series of ten lectures by Paul S. Muhly (which will be published in a CBMS Regional Conference Series volume), twenty-eight lectures were delivered by conference participants on a broad range of topics of current interest in operator algebras and operator theory. This volume contains slightly expanded versions of most of those lectures. Participants were encouraged to bring open problems to the conference, and, as a result, over one hundred problems and questions are scattered throughout this volume. Readers will appreciate this book for the overview it provides of current topics and methods of operator algebras and operator theory.

Zero Product Determined Algebras

Author : Matej Brešar
Publisher : Springer Nature
ISBN 13 : 3030802426
Total Pages : 186 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Zero Product Determined Algebras by : Matej Brešar

Download or read book Zero Product Determined Algebras written by Matej Brešar and published by Springer Nature. This book was released on 2021-08-25 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a concise survey of the theory of zero product-determined algebras, which has been developed over the last 15 years. It is divided into three parts. The first part presents the purely algebraic branch of the theory, the second part presents the functional analytic branch, and the third part discusses various applications. The book is intended for researchers and graduate students in ring theory, Banach algebra theory, and nonassociative algebra.