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Abstract Harmonic Analysis Structure And Analysis For Compact Groups Analysis On Locally Compact Abelian Groups
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Book Synopsis Abstract Harmonic Analysis: Structure and analysis for compact groups, analysis on locally compact Abelian groups by : Edwin Hewitt
Download or read book Abstract Harmonic Analysis: Structure and analysis for compact groups, analysis on locally compact Abelian groups written by Edwin Hewitt and published by . This book was released on 1963 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vol. I. Structure of topological groups, intégration theory group représentations. Vol. II, Structure and analysis for compact groups, Analysis on locally compact abelian groups.
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 2013-11-11 with total page 781 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a continuation of Volume I of the same title [Grund lehren der mathematischen Wissenschaften, Band 115 ]. We constantly 1 1. The textbook Real and cite definitions and results from Volume abstract analysis by E. HEWITT and K. R. STROMBERG [Berlin · Gottin gen ·Heidelberg: Springer-Verlag 1965], which appeared between the publication of the two volumes of this work, contains many standard facts from analysis. We use this book as a convenient reference for such facts, and denote it in the text by RAAA. Most readers will have only occasional need actually to read in RAAA. Our goal in this volume is to present the most important parts of harmonic analysis on compact groups and on locally compact Abelian groups. We deal with general locally compact groups only where they are the natural setting for what we are considering, or where one or another group provides a useful counterexample. Readers who are interested only in compact groups may read as follows: § 27, Appendix D, §§ 28-30 [omitting subheads (30.6)-(30.60)ifdesired], (31.22)-(31.25), §§ 32, 34-38, 44. Readers who are interested only in locally compact Abelian groups may read as follows: §§ 31-33, 39-42, selected Mis cellaneous Theorems and Examples in §§34-38. For all readers, § 43 is interesting but optional. Obviously we have not been able to cover all of harmonic analysis.
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 1979-11-01 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Preliminaries. - Elements of the theory of topolo- gical groups. -Integration on locally compact spaces. - In- variant functionals. - Convolutions and group representa- tions. Characters and duality of locally compact Abelian groups. - Appendix: Abelian groups. Topological linear spa- ces. Introduction to normed algebras. - Bibliography. - In- dex of symbols. - Index of authors and terms.
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 1994-01-20 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: When we acce pted th ekindinvitationof Prof. Dr. F. K. Scnxmrrto write a monographon abstract harmonic analysis for the Grundlehren. der Maihemaiischen Wissenscha/ten series,weintendedto writeall that wecouldfindoutaboutthesubjectin a textof about 600printedpages. We intended thatour book should be accessi ble tobeginners,and we hoped to makeit usefulto specialists as well. These aims proved to be mutually inconsistent. Hencethe presentvolume comprises onl y half of theprojectedwork. Itgives all ofthe structure oftopological groups neededfor harmonic analysisas it is known to u s; it treats integration on locallycompact groups in detail;it contains an introductionto the theory of group representati ons. In the second volume we will treat harmonicanalysisoncompactgroupsand locallycompactAbeliangroups, in considerable et d ail. Thebook is basedon courses given by E. HEWITT at the University of Washington and the University of Uppsala,althoughnaturallythe material of these courses has been en ormously expanded to meet the needsof a formal monograph. Like the. other treatments of harmonic analysisthathaveappeared since 1940,the book is a linealdescendant of A. WEIL'S fundamentaltreatise (WElL [4J)1. The debtof all workers in the field to WEIL'S work is wellknown and enormous. We havealso borrowed freely from LOOMIS'S treatmentof the subject (Lool\IIS[2 J), from NAIMARK [1J,and most especially from PONTRYA GIN [7]. In our exposition ofthestructur e of locally compact Abelian groups and of the PONTRYA GIN-VA N KAM PEN dualitytheorem,wehave beenstrongly influenced byPONTRYA GIN'S treatment. We hope to havejustified the writing of yet anothertreatiseon abstractharmonicanalysis by taking up recentwork, by writingoutthedetailsofeveryimportantconstruction andtheorem,andby including a largenumberof concrete ex amplesand factsnotavailablein other textbooks.
Book Synopsis Abstract Harmonic Analysis by : Edwin Hewitt
Download or read book Abstract Harmonic Analysis written by Edwin Hewitt and published by . This book was released on 1963 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Abstract Harmonic Analysis by : Edwin Hewitt
Download or read book Abstract Harmonic Analysis written by Edwin Hewitt and published by . This book was released on 1963 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 1963-01-01 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: When we accepted the kind invitation of Prof. Dr. F. K. SCHMIDT to write a monograph on abstract harmonie analysis for the Grundlehren der Mathematischen Wissenschaften series, we intended to write aH that we could find out about the subject in a text of about 600 printed pages. We intended that our book should be accessible to beginners, and we hoped to make it useful to specialists as weH. These aims proved to be mutuaHy inconsistent. Hence the present volume comprises only half of the projected work. It gives all of the structure of topologie al groups needed for harmonie analysis as it is known to us; it treats integration on locaHy compact groups in detail; it contains an introduction to the theory of group representations. In the second volume we will treat harmonie analysis on compact groups and locally compact Abelian groups, in considerable detail. The book is based on courses given by E. HEWlTT at the University of Washington and the University of Uppsala, although naturally the material of these courses has been enormously expanded to meet the needs of a formal monograph. Like the other treatments of harmonie analysis that have appeared since 1940, the book is a lineal descendant of A. WEIL'S fundamental treatise (WEIL r 4J) 1. The debt of all workers in the field to WEIL'S work is weH known and enormous.
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
Book Synopsis Gabor Analysis and Algorithms by : Hans G. Feichtinger
Download or read book Gabor Analysis and Algorithms written by Hans G. Feichtinger and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: In his paper Theory of Communication [Gab46], D. Gabor proposed the use of a family of functions obtained from one Gaussian by time-and frequency shifts. Each of these is well concentrated in time and frequency; together they are meant to constitute a complete collection of building blocks into which more complicated time-depending functions can be decomposed. The application to communication proposed by Gabor was to send the coeffi cients of the decomposition into this family of a signal, rather than the signal itself. This remained a proposal-as far as I know there were no seri ous attempts to implement it for communication purposes in practice, and in fact, at the critical time-frequency density proposed originally, there is a mathematical obstruction; as was understood later, the family of shifted and modulated Gaussians spans the space of square integrable functions [BBGK71, Per71] (it even has one function to spare [BGZ75] . . . ) but it does not constitute what we now call a frame, leading to numerical insta bilities. The Balian-Low theorem (about which the reader can find more in some of the contributions in this book) and its extensions showed that a similar mishap occurs if the Gaussian is replaced by any other function that is "reasonably" smooth and localized. One is thus led naturally to considering a higher time-frequency density.
Book Synopsis Principles of Harmonic Analysis by : Anton Deitmar
Download or read book Principles of Harmonic Analysis written by Anton Deitmar and published by Springer. This book was released on 2014-06-21 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a complete and streamlined treatment of the central principles of abelian harmonic analysis: Pontryagin duality, the Plancherel theorem and the Poisson summation formula, as well as their respective generalizations to non-abelian groups, including the Selberg trace formula. The principles are then applied to spectral analysis of Heisenberg manifolds and Riemann surfaces. This new edition contains a new chapter on p-adic and adelic groups, as well as a complementary section on direct and projective limits. Many of the supporting proofs have been revised and refined. The book is an excellent resource for graduate students who wish to learn and understand harmonic analysis and for researchers seeking to apply it.
Book Synopsis Principles of Harmonic Analysis by : Anton Deitmar
Download or read book Principles of Harmonic Analysis written by Anton Deitmar and published by Springer Science & Business Media. This book was released on 2008-11-21 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The tread of this book is formed by two fundamental principles of Harmonic Analysis: the Plancherel Formula and the Poisson S- mation Formula. We ?rst prove both for locally compact abelian groups. For non-abelian groups we discuss the Plancherel Theorem in the general situation for Type I groups. The generalization of the Poisson Summation Formula to non-abelian groups is the S- berg Trace Formula, which we prove for arbitrary groups admitting uniform lattices. As examples for the application of the Trace F- mula we treat the Heisenberg group and the group SL (R). In the 2 2 former case the trace formula yields a decomposition of the L -space of the Heisenberg group modulo a lattice. In the case SL (R), the 2 trace formula is used to derive results like the Weil asymptotic law for hyperbolic surfaces and to provide the analytic continuation of the Selberg zeta function. We ?nally include a chapter on the app- cations of abstract Harmonic Analysis on the theory of wavelets. The present book is a text book for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up of the First Course in Harmonic Analysis, [9], or indep- dently, if the students have required a modest knowledge of Fourier Analysis already. In this book, among other things, proofs are given of Pontryagin Duality and the Plancherel Theorem for LCA-groups, which were mentioned but not proved in [9].
Book Synopsis Abstract Harmonic Analysis: Structure of topological groups, integration theory, group representations by : Edwin Hewitt
Download or read book Abstract Harmonic Analysis: Structure of topological groups, integration theory, group representations written by Edwin Hewitt and published by . This book was released on 1963 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
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.
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.
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.
Book Synopsis Aspects of Harmonic Analysis on Locally Compact Abelian Groups by : Jean H Gallier
Download or read book Aspects of Harmonic Analysis on Locally Compact Abelian Groups written by Jean H Gallier and published by . This book was released on 2024-06-14 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Fourier transform is a 'tool' used in engineering and computer vision to model periodic phenomena. Starting with the basics of measure theory and integration, this book delves into the harmonic analysis of locally compact abelian groups. It provides an in-depth tour of the beautiful theory of the Fourier transform based on the results of Gelfand, Pontrjagin, and Andre Weil in a manner accessible to an undergraduate student who has taken linear algebra and introductory real analysis.Highlights of this book include the Bochner integral, the Haar measure, Radon functionals, the theory of Fourier analysis on the circle, and the theory of the discrete Fourier transform. After studying this book, the reader will have the preparation necessary for understanding the Peter-Weyl theorems for complete, separable Hilbert algebras, a key theoretical concept used in the construction of Gelfand pairs and equivariant convolutional neural networks.
