CONTENTS
List of Figures viii
Index of Notation ix
Abstract xi
Chapter 0. Introduction 1
Chapter 1. The Green Function 6
1. Random Walks on a Tree 6
2. The Method of Paths 8
3. The Nearest Neighbor Case 10
4. The Case of a Finitely Supported Measure 11
5. Algebraicity of the Green Function 13
6. Notes and Remarks 15
Chapter 2. The Spectrum and the Plancherel Measure 17
1. The Spectrum of the Random Walk in C{G) 17
2. The
£2-spectrum
and the Real
£l
-spectrum 21
3. The Plancherel Formula 26
4. Notes and Remarks 30
Chapter 3. Representations and their Realization on the
Boundary 31
1. Boundary Theory for Eigenfunctions of the Random Walk 31
2. The Principal Series 34
3. The Complementary Series 39
4. Notes and Remarks 54
Chapter 4. Irreducibility and Inequivalence 56
1. Irreducibility 56
2. Inequivalence 61
3. Notes and Remarks 65
References 66
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