Harmonic Analysis on Free Groups

This book presents an account of recent results on the theory of representations and the harmonic analysis of free groups. It emphasizes the analogy with the theory of representations of noncompact semisimple Lie groups and restricts the focus to a class of irreducible unitary representations. 1. Introduction 2. Convolution Theorems 3. Spherical Functions 4. Eigenfunctions of the Laplace Operator and Representations 5. Unitary Representations 6. Uniformly Bounded Representations 7. Local Limit Theorems and Unitary Representations 8. Algebras of Coefficients of Representations