Unitary Representations and Harmonic Analysis: An Introduction (Volume 44) (North-Holland Mathematical Library, Volume 44)

Unitary Representations and Harmonic Analysis
Copyright Page
Preface to the Second Edition
Preface
Contents
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)
	§4. Enumeration of irreducible representations
	§5. 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
	§1. Construction of irreducible representations
	§2. 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
	§10. Irreducible unitary representations of SL (2, R)
Appendix
Notes
Bibliography
Index