Interpolation in Model Spaces

TL;DR

This paper investigates interpolation properties in model spaces formed by the orthogonal complement of Blaschke products in Hardy space, focusing on the behavior of interpolating sequences and their perturbations.

Contribution

It provides new insights into how unions of interpolating sequences behave in model spaces, especially under pseudohyperbolic distance conditions and sequence perturbations.

Findings

Unions of interpolating sequences can be characterized based on their pseudohyperbolic distance.

Sequences far apart in the pseudohyperbolic metric maintain interpolation properties.

Perturbations of Frostman sequences affect their interpolation behavior.

Abstract

In this paper we consider interpolation in model spaces, $H^2 \ominus B H^2$ with $B$ a Blaschke product. We study unions of interpolating sequences for two sequences that are far from each other in the pseudohyperbolic metric as well as two sequences that are close to each other in the pseudohyperbolic metric. The paper concludes with a discussion of the behavior of Frostman sequences under perturbations.