000			01986nam a22003017a 4500
003			OSt
005			20250729173107.0
008			250729b |||||||| |||| 00| 0 eng d
020			_a9780387228372
020			_a9781493976287 (pbk.) _c€ 69.99
040			_bENG _cIISER-BPR _dIISER-BPR
041			_aENG
082			_a515.2433 _bDEI _223rd
100			_aDeitmar, Anton _95500
222			_aMathematics
245			_aA first course in harmonic analysis
250			_a2nd ed.
260			_aNew York : _bSpringer-Verlag New York, Inc., _cc2005
300			_axii, 192 p. : _c23cm
440			_aUniversitext
504			_aIncludes appendices, bibliographic references and subject 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.
650			_aMathematics
650			_aAnalysis
650			_aGeneral aspects of analysis _95501
650			_aHarmonic analysis
942			_2ddc _cBK
999			_c4278 _d4278