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020			_a9781493976287
040			_aNISER LIBRARY _cNISER LIBRARY _beng
082	0	0	_a517.57 _bDEI-F
100	1		_aDeitmar, Anton
245	1	0	_aFirst course in harmonic analysis
250			_a2nd edition
260			_aNew York : _bSpringer, _c2005.
300			_axii, 192 pages : _billustrations ; _c24 cm.
490	0		_aUniversitext
504			_aIncludes bibliographical references (p. 187-189) and index.
520			_aThe second part of the book concludes with Plancherel’s theorem in Chapter 8. This theorem is a generalization of the completeness of the Fourier series, as well as of Plancherel’s theorem for the real line. The third part of the book is intended to provide the reader with a ?rst impression of the world of non-commutative harmonic analysis. Chapter 9 introduces methods that are used in the analysis of matrix groups, such as the theory of the exponential series and Lie algebras. These methods are then applied in Chapter 10 to arrive at a clas- ?cation of the representations of the group SU(2). In Chapter 11 we give the Peter-Weyl theorem, which generalizes the completeness of the Fourier series in the context of compact non-commutative groups and gives a decomposition of the regular representation as a direct sum of irreducibles. The theory of non-compact non-commutative groups is represented by the example of the Heisenberg group in Chapter 12. The regular representation in general decomposes as a direct integral rather than a direct sum. For the Heisenberg group this decomposition is given explicitly. Acknowledgements: I thank Robert Burckel and Alexander Schmidt for their most useful comments on this book. I also thank Moshe Adrian, Mark Pavey, Jose Carlos Santos, and Masamichi Takesaki for pointing out errors in the ?rst edition. Exeter, June 2004 Anton Deitmar LEITFADEN vii Leitfaden 1 2 3 5 4 6
650		0	_aHarmonic analysis
650		0	_aFourier analysis
650		0	_aFourier transform
650		0	_aHilbert space
650		0	_aRiemann integral
650		0	_aMatrix
856	4	1	_3Electronic version _uhttps://link.springer.com/book/10.1007/0-387-27561-4
856	4	1	_3Table of contents _uhttps://link.springer.com/content/pdf/bfm:978-0-387-27561-1/1
856	4	1	_3Reviews _uhttps://www.goodreads.com/book/show/1982241.A_First_Course_in_Harmonic_Analysis#CommunityReviews
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999			_c36034 _d36034