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Aspects Of Harmonic Analysis On Locally Compact Abelian Groups
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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 World Scientific. This book was released on 2024-06-21 with total page 760 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.
Author :Jocelyn Quaintance Jean Gallier Publisher :World Scientific Publishing Company ISBN 13 :9789811291715 Total Pages :0 pages Book Rating :4.2/5 (917 download)
Book Synopsis Aspects of Harmonic Analysis on Locally Compact Abelian Groups by : Jocelyn Quaintance Jean Gallier
Download or read book Aspects of Harmonic Analysis on Locally Compact Abelian Groups written by Jocelyn Quaintance Jean Gallier and published by World Scientific Publishing Company. This book was released on 2024 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "A rigorous, accessible, and self-contained introduction to the harmonic analysis of locally compact abelian groups and the mathematical underpinnings of the Fourier transform"--
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 Abstract Harmonic Analysis by : Edwin J. Hewitt
Download or read book Abstract Harmonic Analysis written by Edwin J. Hewitt and published by . This book was released on 1970 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 2014-01-15 with total page 788 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 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 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Self-contained treatment by a master mathematical expositor ranges from introductory chapters on basic theorems of Fourier analysis and structure of locally compact Abelian groups to extensive appendixes on topology, topological groups, more. 1962 edition.
Book Synopsis Harmonic Analysis on Locally Compact Abelian Groups by : Alan Alfred Townley
Download or read book Harmonic Analysis on Locally Compact Abelian Groups written by Alan Alfred Townley and published by . This book was released on 1977 with total page 196 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 1970 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Potential Theory on Locally Compact Abelian Groups by : C. van den Berg
Download or read book Potential Theory on Locally Compact Abelian Groups written by C. van den Berg and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: Classical potential theory can be roughly characterized as the study of Newtonian potentials and the Laplace operator on the Euclidean space JR3. It was discovered around 1930 that there is a profound connection between classical potential 3 theory and the theory of Brownian motion in JR . The Brownian motion is determined by its semigroup of transition probabilities, the Brownian semigroup, and the connection between classical potential theory and the theory of Brownian motion can be described analytically in the following way: The Laplace operator is the infinitesimal generator for the Brownian semigroup and the Newtonian potential kernel is the" integral" of the Brownian semigroup with respect to time. This connection between classical potential theory and the theory of Brownian motion led Hunt (cf. Hunt [2]) to consider general "potential theories" defined in terms of certain stochastic processes or equivalently in terms of certain semi groups of operators on spaces of functions. The purpose of the present exposition is to study such general potential theories where the following aspects of classical potential theory are preserved: (i) The theory is defined on a locally compact abelian group. (ii) The theory is translation invariant in the sense that any translate of a potential or a harmonic function is again a potential, respectively a harmonic function; this property of classical potential theory can also be expressed by saying that the Laplace operator is a differential operator with constant co efficients.
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 Structure and Analysis for Compact Groups, Analysis on Locally Compact Abelian Groups by : Edwin Hewitt
Download or read book Structure and Analysis for Compact Groups, Analysis on Locally Compact Abelian Groups written by Edwin Hewitt and published by . This book was released on 1970 with total page 771 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Abstract Harmonic Analysis. Vol. II by : Edwin Hewitt
Download or read book Abstract Harmonic Analysis. Vol. II written by Edwin Hewitt and published by . This book was released on 1970 with total page 771 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Harmonic And Spectral Analysis by : Laszlo Szekelyhidi
Download or read book Harmonic And Spectral Analysis written by Laszlo Szekelyhidi and published by World Scientific. This book was released on 2014-03-19 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a modern introduction to harmonic analysis and synthesis on topological groups. It serves as a guide to the abstract theory of Fourier transformation. For the first time, it presents a detailed account of the theory of classical harmonic analysis together with the recent developments in spectral analysis and synthesis.
Book Synopsis Classical Harmonic Analysis and Locally Compact Groups by : Hans Reiter
Download or read book Classical Harmonic Analysis and Locally Compact Groups written by Hans Reiter and published by Oxford University Press on Demand. This book was released on 2000 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: A revised and expanded second edition of Reiter's classic text Classical Harmonic Analysis and Locally Compact Groups (Clarendon Press 1968). It deals with various developments in analysis centring around around the fundamental work of Wiener, Carleman, and especially A. Weil. It starts with the classical theory of Fourier transforms in euclidean space, continues with a study at certain general function algebras, and then discusses functions defined on locally compact groups. The aim is, firstly, to bring out clearly the relations between classical analysis and group theory, and secondly, to study basic properties of functions on abelian and non-abelian groups. The book gives a systematic introduction to these topics and endeavours to provide tools for further research. In the new edition relevant material is added that was not yet available at the time of the first edition.
Book Synopsis An Operational Method for Harmonic Analysis on Locally Compact Abelian Group by : Hisaharu Umegaki
Download or read book An Operational Method for Harmonic Analysis on Locally Compact Abelian Group written by Hisaharu Umegaki and published by . This book was released on 1967 with total page 47 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 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.
