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Field name	Details
Dewey Class	515.785
Title	Principles of Harmonic Analysis (EB) / by Anton Deitmar, Siegfried Echterhoff.
Author	Deitmar, Anton
Added Personal Name	Echterhoff, Siegfried
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : Springer , 2009.
Physical Details	: online resource.
Series	Universitext
ISBN	9780387854694
Summary Note	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 TÃ¼bingen, 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 MÃ¼nster, Germany.:
Contents note	Preface -- 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(R) -- Wavelets -- Topology -- Measure and Integration -- Functional Analysis -- Bibliography -- Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-0-387-85469-4
Links to Related Works	Subject References: Abstract Harmonic Analysis . Fourier Analysis . Harmonic analysis . Mathematics . Authors: author . Deitmar, Anton . Echterhoff, Siegfried . Corporate Authors: SpringerLink (Online service) . Series: Universitext . Classification: 515.785 .

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Principles of Harmonic Analysis

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