The principal aim of this book is to give an introduction to harmonic analysis and the theory of unitary representations of Lie groups. The second edition has been brought up to date with a number of textual changes in each of the five chapters, a new appendix on Fatou's theorem has been added in connection with the limits of discrete series, and the bibliography has been tripled in length.
Author(s): Mitsuo Sugiura
Series: North-Holland Mathematical Library 44
Edition: 2 Sub
Publisher: North-Holland
Year: 1990
Language: English
Pages: 469
Unitary Representations and Harmonic Analysis......Page 4
Copyright Page......Page 5
Preface to the Second Edition......Page 8
Preface......Page 10
Contents......Page 14
Conventions and Notations......Page 16
§1. Introduction......Page 18
§2. Fundamental definitions......Page 22
§3. Unitary representations of compact groups......Page 31
§4. Fourier series of square integrable functions......Page 47
§5. Fourier series of smooth functions and distributions......Page 51
§1. Construction of irreducible representations of SU(2)......Page 64
§2. Characters of compact groups......Page 67
§3. Haar measures on SU(2)......Page 71
§4. Enumeration of irreducible representations......Page 74
§5. Lie algebras and their representations......Page 76
§6. Fourier series on SU(2)......Page 93
§7. Representations of SO(3) and spherical harmonics......Page 99
§8. Fourier series on compact Lie groups......Page 110
§1. Rapidly decreasing functions......Page 118
§2. The Plancherel theorem and the decomposition of the regular representation......Page 132
§3. Positive definite functions and Stone’s theorem......Page 139
§4. The Paley-Wiener theorem......Page 159
§5. Tempered distributions and their Fourier transforms......Page 167
§1. Construction of irreducible representations......Page 172
§2. Classification of irreducible unitary representations......Page 182
§3. Fourier transforms of rapidly decreasing functions......Page 186
§4. The Plancherel theorem......Page 196
§5. Determination of g(G) and D(G)......Page 204
§1. The Iwasawa decomposition......Page 222
§2. Irreducible unitary representations......Page 230
§3. Irreducible unitary representations......Page 252
§4. Irreducible unitary representations......Page 272
§5. K-finite vectors......Page 282
§6. Classification of irreducible unitary representations......Page 297
§7. The characters......Page 323
§8. Inversion formula......Page 360
§9. Harmonic analysis of zonal functions......Page 379
§10. Irreducible unitary representations of SL (2, R)......Page 405
Appendix......Page 412
Notes......Page 428
Bibliography......Page 434
Index......Page 466
