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Tables of Contents for Harmonic Analysis on Free Groups
Chapter/Section Title
Page #
Page Count
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