Electronic ISBN:  9781470401108 
Product Code:  MEMO/110/531.E 
List Price:  $36.00 
MAA Member Price:  $32.40 
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Book DetailsMemoirs of the American Mathematical SocietyVolume: 110; 1994; 68 ppMSC: Primary 22; Secondary 20; 43; 60;
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.
ReadershipResearch mathematicians.

Table of Contents

Chapters

0. Introduction

1. The Green function

2. The spectrum and the Plancherel measure

3. Representations and their realization on the boundary

4. Irreducibility and inequivalence


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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.
Research mathematicians.

Chapters

0. Introduction

1. The Green function

2. The spectrum and the Plancherel measure

3. Representations and their realization on the boundary

4. Irreducibility and inequivalence