Elements Of Abstract Harmonic Analysis
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Elements of Abstract Harmonic Analysis
Author | : George Bachman |
Publsiher | : Elsevier |
Total Pages | : 269 |
Release | : 2013-10-22 |
Genre | : Mathematics |
ISBN | : 9781483267562 |
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Elements of Abstract Harmonic Analysis provides an introduction to the fundamental concepts and basic theorems of abstract harmonic analysis. In order to give a reasonably complete and self-contained introduction to the subject, most of the proofs have been presented in great detail thereby making the development understandable to a very wide audience. Exercises have been supplied at the end of each chapter. Some of these are meant to extend the theory slightly while others should serve to test the reader's understanding of the material presented. The first chapter and part of the second give a brief review of classical Fourier analysis and present concepts which will subsequently be generalized to a more abstract framework. The next five chapters present an introduction to commutative Banach algebras, general topological spaces, and topological groups. The remaining chapters contain some of the measure theoretic background, including the Haar integral, and an extension of the concepts of the first two chapters to Fourier analysis on locally compact topological abelian groups.
Introduction to Abstract Harmonic Analysis
Author | : Lynn H. Loomis |
Publsiher | : Courier Corporation |
Total Pages | : 210 |
Release | : 2011-06-01 |
Genre | : Mathematics |
ISBN | : 9780486481234 |
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"Harmonic analysis is a branch of advanced mathematics with applications in such diverse areas as signal processing, medical imaging, and quantum mechanics. This classic monograph is the work of a prominent contributor to the field. Geared toward advanced undergraduates and graduate students, it focuses on methods related to Gelfand's theory of Banach algebra. 1953 edition"--
Abstract Harmonic Analysis
Author | : Edwin Hewitt,Kenneth A. Ross |
Publsiher | : Springer |
Total Pages | : 525 |
Release | : 1994-01-20 |
Genre | : Mathematics |
ISBN | : 9780387941905 |
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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.
A Course in Abstract Harmonic Analysis
Author | : Gerald B. Folland |
Publsiher | : CRC Press |
Total Pages | : 317 |
Release | : 2016-02-03 |
Genre | : Mathematics |
ISBN | : 9781498727150 |
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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
Functional Analysis
Author | : George Bachman,Lawrence Narici |
Publsiher | : Courier Corporation |
Total Pages | : 548 |
Release | : 2000-01-01 |
Genre | : Mathematics |
ISBN | : 0486402517 |
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Excellent treatment of subject geared toward students with background in linear algebra, advanced calculus, physics and engineering. Text covers introduction to inner-product spaces, normed, metric spaces, and topological spaces; complete orthonormal sets, the Hahn-Banach Theorem and its consequences, and many other related subjects. Includes detailed proofs of theorems, bibliography, and index of symbols. 1966 edition.
An Introduction to Abstract Harmonic Analysis
Author | : Lynn H. Loomis |
Publsiher | : Franklin Classics Trade Press |
Total Pages | : 202 |
Release | : 2018-11-10 |
Genre | : History |
ISBN | : 0353241822 |
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This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Abstract Harmonic Analysis
Author | : Edwin Hewitt,Kenneth A. Ross |
Publsiher | : Unknown |
Total Pages | : 784 |
Release | : 2014-09-01 |
Genre | : Electronic Book |
ISBN | : 3642620094 |
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Abstract Harmonic Analysis
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Author | : Edwin Hewitt,Kenneth A. Ross |
Publsiher | : Unknown |
Total Pages | : 135 |
Release | : 1987 |
Genre | : Electronic Book |
ISBN | : OCLC:797068473 |
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