Aut([[inline]]) – Its Haar Measure and a unitary representation: a constructive approach

Abstract

We endow the set of all automorphisms Aut of the open unit ball in C n with an structure of a locally compact topological group and we give an explicit characterization of the Haar measure on the group Aut which turns out to be unimodular.We also establish a unitary representation for Aut and describe the corresponding operator-valued Fourier transform. Although these properties of Aut can be obtained as consequences of general results in Harmonic Analysis, the proofs we present in this manuscript are self contained and mainly based on Classical Analysis.