TY  - BOOK
AU  - Deitmar, Anton
TI  - A first course in harmonic analysis
SN  - 9780387228372
U1  - 515.2433 23rd
PY  - 2005///
CY  - New York
PB  - Springer-Verlag New York, Inc.
KW  - Mathematics
KW  - Analysis
KW  - General aspects of analysis
KW  - Harmonic analysis
N1  - Includes appendices, bibliographic references and subject index
N2  - The 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
ER  -