Harmonic Analysis and Representation Theory for Groups Acting on Homogenous Trees

by Alessandro Figá-Talamanca, Claudio Nebbia

Overview

These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree. The unitary irreducible representations are classified in three types: a continuous series of spherical representations; two special representations; and a countable series of cuspidal representations as defined by G.I. Ol'shiankii. Several notable subgroups of the full automorphism group are also considered. The theory of spherical functions as eigenvalues of a Laplace (or Hecke) operator on the tree is used to introduce spherical representations and their restrictions to discrete subgroups. This will be an excellent companion for all researchers into harmonic analysis or representation theory.

Product Details

ISBN-13:	9780521424448
Publisher:	Cambridge University Press
Publication date:	06/28/1991
Series:	London Mathematical Society Lecture Note Series , #162
Pages:	164
Product dimensions:	5.98(w) x 8.98(h) x 0.39(d)

Table of Contents

Chapter 1; Chapter 2; Chapter 3; Appendix