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Principles of Harmonic Analysis 2009 Edition
Contributor(s): Deitmar, Anton (Author), Echterhoff, Siegfried (Author)

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 ISBN: 0387854681     ISBN-13: 9780387854687
Publisher: Springer
OUR PRICE: $66.49  

Binding Type: Paperback - See All Available Formats & Editions
Published: November 2008
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Additional Information
BISAC Categories:
- Mathematics | Mathematical Analysis
Dewey: 515.243
LCCN: 2008938333
Series: Universitext
Physical Information: 0.8" H x 6.1" W x 9.1" L (1.10 lbs) 352 pages
Features: Bibliography, Index, Table of Contents
 
Descriptions, Reviews, Etc.
Publisher Description:
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].
 
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