# Eric Schippers

## Operator representations of families of one-to-one holomorphic maps

Date Friday, March 28, 2008

Holomorphic mappings can often be represented as operators on Hilbert spaces. Thus function theory provides examples of operators, and conversely the operator representation can shed light on the family of mappings.

I will outline some basic results about operator representations of families of injective holomorphic functions. The condition that the maps be injective can be expressed as a simple operator inequality. This talk is an overview; proofs and technical details will be minimized.