UID:
almahu_9947367998602882
Format:
1 online resource (469 p.)
Edition:
2nd ed.
ISBN:
1-281-78309-9
,
9786611783099
,
0-08-088759-7
Series Statement:
North-Holland mathematical library ; v. 44
Content:
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.
Note:
Description based upon print version of record.
,
Front Cover; Unitary Representations and Harmonic Analysis; Copyright Page; Contents; Preface to the Second Edition; Preface; Conventions and Notations; Chapter I. Fourier series and the torus group T; 1. Introduction; 2. Fundamental definitions; 3. Unitary representations of compact groups; 4. Fourier series of square integrable functions; 5. Fourier series of smooth functions and distributions; Chapter II. Representations of SU(2) and SO(3); 1. Construction of irreducible representations of SU(2); 2. Characters of compact groups; 3. Haar measures on SU(2)
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4. Enumeration of irreducible representations5. Lie algebras and their representations; 6. Fourier series on SU(2); 7. Representations of SO(3) and spherical harmonics; 8. Fourier series on compact Lie groups; Chapter III. The Fourier transform and unitary representations of Rn; 1. Rapidly decreasing functions; 2. The Plancherel theorem and the decomposition of the regular representation; 3. Positive definite functions and Stone's theorem; 4. The Paley-Wiener theorem; 5. Tempered distributions and their Fourier transforms; Chapter IV. The Euclidean motion group
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1. Construction of irreducible representations2. Classification of irreducible unitary representations; 3. Fourier transforms of rapidly decreasing functions; 4. The Plancherel theorem; 5. Determination of g(G) and D(G); Chapter V. Unitary representation of SL(2, R); 1. The Iwasawa decomposition; 2. Irreducible unitary representations; 3. Irreducible unitary representations; 4. Irreducible unitary representations; 5. K-finite vectors; 6. Classification of irreducible unitary representations; 7. The characters; 8. Inversion formula; 9. Harmonic analysis of zonal functions
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10. Irreducible unitary representations of SL (2, R)Appendix; Notes; Bibliography; Index
,
English
Additional Edition:
ISBN 0-444-88593-5
Language:
English
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