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E-grāmata: Harmonic Analysis on Free Groups [Taylor & Francis e-book]

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Harmonic Analysis on Free GroupsPalielināt
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This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations.
Preface iii
List of Symbols
vii
Introduction
1(10)
Free Groups and Free Sets
1(2)
Unitary Representations of Discrete Groups
3(3)
The Regular Representation
6(5)
Convolution Theorems
11(20)
Haagerup's Convolution Theorem
11(3)
Simplicity of Cλ* (Fr)
14(2)
An Exact Computation
16(12)
Notes and Remarks
28(3)
Spherical Functions
31(20)
Radial Functions
31(3)
The Poisson Kernel
34(6)
The Spectrum of Radial Functions
40(4)
The Plancherel Measure
44(2)
Notes and Remarks
46(5)
Eigenfunctions of The Laplace Operator and Representations
51(18)
The Poisson Transform
51(3)
Cylindrical Functions and Martingales on the Poisson Boundary
54(2)
Eigenfunctions of the Laplace Operator
56(7)
Intertwining Operators
63(4)
Notes and Remarks
67(2)
Unitary Representations
69(22)
The Principal and Complementary Series
69(3)
Distribution of Values of Translates of Spherical Functions
72(4)
Irreducibility
76(10)
Decomposition of the Regular Representation
86(2)
Notes and Remarks
88(3)
Uniformly Bounded Representations
91(12)
An Intergral Kernel for Intertwining Operators
91(5)
Lorentz Spaces
96(4)
Uniform Boundedness
100(2)
Notes and Remarks
102(1)
Local Limit Theorems and Unitary Representations
103(16)
Local Properties of Spherical Functions
103(3)
Convolution Powers of Radial Probability Measures
106(5)
Local Limit Theorems and Complementary Series
111(3)
Notes and Remarks
114(5)
Algebras of Coefficients of Representations
119(18)
The Fourier Algebra
119(3)
The Radial Fourier-Stieltjes Algebra
122(3)
A Class of Positive Definite Functions
125(4)
Convolution Operators and Ap Algebras
129(6)
Notes and Remarks
135(2)
References 137(6)
Index 143
Alessandro Figa-Talamanca is Professor of Mathematical Analysis at the University of Rome, Italy.
Permanent link: https://www.kriso.lv/db/9781003071747_pe.html
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