Athanasios Beslikas: Composition Operators and Rational Inner Functions on the Bidisc: A Geometric Approach

Abstract:  In this talk, we will discuss the boundedness of composition operators acting on spaces of holomorphic functions on the bidisc, focusing particularly on weighted Bergman spaces and holomorphic self-maps involving rational inner functions. While the theory of composition operators in one complex variable is well understood, the passage to several variables introduces new difficulties, closely related to the geometry of the underlying domains.

Our approach is based on studying the level sets of rational inner functions and their intersections near the boundary of the bidisc. In particular, we will explain how transversal and tangential intersections lead to different operator-theoretic behavior. We will illustrate this through some examples.