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＜電子ブック＞
Principles of Harmonic Analysis / by Anton Deitmar, Siegfried Echterhoff
(Universitext. ISSN:21916675)

版	1st ed. 2009.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2009
本文言語	英語
大きさ	XV, 333 p : online resource
著者標目	*Deitmar, Anton author Echterhoff, Siegfried author SpringerLink (Online service)
件　名	LCSH:Harmonic analysis LCSH:Fourier analysis FREE:Abstract Harmonic Analysis FREE:Fourier Analysis
一般注記	Haar Integration -- Banach Algebras -- Duality for Abelian Groups -- The Structure of LCA-Groups -- Operators on Hilbert Spaces -- Representations -- Compact Groups -- Direct Integrals -- The Selberg Trace Formula -- The Heisenberg Group -- SL2(?) -- Wavelets The present book is intended as a text for a graduate course on abstract harmonic analysis and its applications. The book can be used as a follow up to Anton Deitmer's previous book, A First Course in Harmonic Analysis, or independently, if the students already have a modest knowledge of Fourier Analysis. 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 A First Course in Harmonic Analysis. Using Pontryagin duality, the authors also obtain various structure theorems for locally compact abelian groups. The book then proceeds with Harmonic Analysis on non-abelian groups and its applications to theory in number theory and the theory of wavelets. Knowledge of set theoretic topology, Lebesgue integration, and functional analysis on an introductory level will be required in the body of the book. For the convenience of the reader, all necessary ingredients from these areas have been included in the appendices. Professor Deitmar is Professor of Mathematics at the University of Tübingen, Germany. He is a former Heisenberg fellow and has taught in the U.K. for some years. Professor Echterhoff is Professor of Mathematics and Computer Science at the University of Münster, Germany HTTP:URL=https://doi.org/10.1007/978-0-387-85469-4

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