Compact composition operators on weighted Hilbert spaces of analytic functions

TL;DR

This paper characterizes when composition operators are compact on a broad class of weighted Hilbert spaces of analytic functions, using generalized Nevanlinna counting functions, bridging the gap between Bergman and Dirichlet spaces.

Contribution

It provides a new characterization of compactness for composition operators on weighted Hilbert spaces via generalized Nevanlinna counting functions.

Findings

Characterization of compactness in terms of Nevanlinna counting functions

Applicable to a large class of Hilbert spaces between Bergman and Dirichlet spaces

Extends understanding of composition operators in complex analysis

Abstract

We characterize the compactness of composition operators; in term of generalized Nevanlinna counting functions, on a large class of Hilbert spaces of analytic functions, which can be viewed between the Bergman and the Dirichlet spaces