Analytic functions on the bidisk at boundary singularities via Hilbert space methods

TL;DR

This paper studies the boundary behavior of Schur class functions on the bidisk using Hilbert space models, providing geometric conditions that classify their boundary derivatives at singular points.

Contribution

It introduces a geometric condition on associated operators that characterizes the boundary derivative behavior of Schur functions at singular boundary points.

Findings

Boundary behavior linked to Hilbert space model geometry

Classification of directional derivatives at boundary singularities

Conditions for growth at boundary points

Abstract

We investigate the behavior of a generalized Hilbert space model of a function in the Schur class of the bidisk at singular boundary points that satisfy a growth condition. We examine the relationship between the boundary behavior of Schur functions and the geometry of corresponding generalized Hilbert space models. We describe a geometric condition on an associated operator that classifies the behavior of the directional derivative of the underlying Schur function at a carapoint.