**Professor Pietro Poggi-Corradini**

Kansas State University

**"Norm convergence of normalized iterates and the growth of Koenigs maps"**

**Abstract:**

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.

#### Friday, November 20, 1998

3:00 PM in 335 Jabara Hall

Please join us for refreshments before the lecture at 2:30p.m. in room 353 Jabara Hall.

[ Fall 1998]