Kansas State University
Let be an analytic function defined on the unit disk U such that . Write to denote the map composed with itself n times. Then and . A classical result of Koenigs shows that the sequence of normalized iterates converges uniformly on compact subsets of to an analytic function such that . We will discuss some properties of the Koenigs map which arise in the theory of composition operators. More specifically, the function is an eigenfunction for the composition operator . These operators are bounded on the classical Hardy and Bergman spaces. It is therefore important to know when does belong to these spaces and when does the sequence converge to in the corresponding norm.
Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.
[ Fall 1998]