**Memoirs of the American Mathematical Society**

1994;
68 pp;
Softcover

MSC: Primary 22;
Secondary 20; 43; 60

Print ISBN: 978-0-8218-2594-5

Product Code: MEMO/110/531

List Price: $36.00

Individual Member Price: $21.60

**Electronic ISBN: 978-1-4704-0110-8
Product Code: MEMO/110/531.E**

List Price: $36.00

Individual Member Price: $21.60

# Harmonic Analysis for Anisotropic Random Walks on Homogeneous Trees

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*Alessandro Figà-Talamanca; Tim Steger*

This work presents a detailed study of the anisotropic series representations of the free product group \(\mathbf Z/2\mathbf Z\star \cdots \star \mathbf Z/2\mathbf Z\). These representations are infinite dimensional, irreducible, and unitary and can be divided into principal and complementary series. Anisotropic series representations are interesting because, while they are not restricted from any larger continuous group in which the discrete group is a lattice, they nonetheless share many properties of such restrictions. The results of this work are also valid for nonabelian free groups on finitely many generators.

#### Table of Contents

# Table of Contents

## Harmonic Analysis for Anisotropic Random Walks on Homogeneous Trees

- Contents vii8 free
- List of Figures viii9 free
- Index of Notation ix10 free
- Abstract xi12 free
- Chapter 0. Introduction 114 free
- Chapter 1. The Green Function 619 free
- Chapter 2. The Spectrum and the Plancherel Measure 1730
- Chapter 3. Representations and their Realization on the Boundary 3144
- Chapter 4. Irreducibility and Inequivalence 5669
- References 6679

#### Readership

Research mathematicians.