The Structure of Groups of Analytic Transformations

Abstract

n this thesis we review some classical results by H. Cartan, devoted to the study of certain families of real-analytic and holomorphic diffeomorphisms. In particular, it is shown that a local, quasi-continuous group of holomorphic transformations has the structure of a local Lie group. In turn, this implies that the automorphism group of a bounded domain in C^n is a (finite dimensional) Lie group.