# Composition Operators on Spaces of Analytic Functions

# Composition Operators on Spaces of Analytic Functions

**Description:** There are many examples of Banach and
Hilbert spaces of analytic functions

on the unit disk or the unit ball in complex N -space. For a fixed analytic map
of the

disk or the ball into itself, composition of functions in the space with this
map is a linear

transformation on the space, called a composition operator . The overall goal of
study in

this area is to connect the properties of this transformation as a linear
operator with the

geometric and analytic properties of the underlying map of the disk or ball.

This course will present :

1) fundamentals from complex analysis such as results on fixed points,
iteration,

and behavior at the boundary

2) results concerning Banach and Hilbert spaces of analytic functions

3) fundamentals from operator theory important for this area

4) basic results on boundedness, compactness, and spectra of composition
operators .

**Text: **Cowen and MacCluer Composition Operators on Spaces of Analytic
Functions

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