A brief introduction to composition operators

A composition operator is an infinite-dimensional linear transformation that acts on a Hilbert space of analytic functions. Applying a composition operator associated with a fixed function, or symbol, to an analytic function results in the function composition of the analytic function and the symbol. In this talk, we study the basic properties of composition operators (primarily on the Hardy Hilbert space) and their adjoints as they relate to the symbol.

Further reading: Cowen–MacCluer, Composition Operators on Spaces of Analytic Functions (Routledge, 2019).