Principles of Harmonic Analysis PDF
by Anton Deitmar, Siegfried Echterhoff
Part of the Universitext series
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].
Information
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Download - Immediately Available
- Format:PDF
- Publisher:Springer New York
- Publication Date:04/12/2008
- Category:
- ISBN:9780387854694
Other Formats
- Paperback / softback from £45.59
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Information
-
Download - Immediately Available
- Format:PDF
- Publisher:Springer New York
- Publication Date:04/12/2008
- Category:
- ISBN:9780387854694
