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020			_a9781071646328
040			_aNISER LIBRARY _beng _cNISER LIBRARY
082			_a517.57 _bDEI-P
100	1		_aDeitmar, Anton
245			_aPrinciples of harmonic analysis
260			_aNew York, NY : _bSpringer, _c2009.
300			_axv, 333 pages ; _c24 cm.
490			_aUniversitext
504			_aIncludes bibliographical references (pages 323-327) and index.
520			_aThe 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].
650			_aHarmonic analysis
650			_aAbelian group
650			_aFourier series
650			_aHilbert space
650			_aFunctional analysis
650			_aTopology
700	1		_aEchterhoff, Siegfried
856			_3Electronic version _uhttps://link.springer.com/book/10.1007/978-0-387-85469-4
856			_3Table of contents _uhttps://link.springer.com/content/pdf/bfm:978-0-387-85469-4/1
856			_3Reviews _uhttps://www.goodreads.com/book/show/5753132-principles-of-harmonic-analysis?ref=nav_sb_ss_1_13#CommunityReviews
942			_2udc _cN
999			_c36033 _d36033