Szeg\"o type results relative to a sequence of model spaces

TL;DR

This paper generalizes the classical Szeg"o theorem by exploring its validity and implications for sequences of powers of finite Blaschke products, extending the theorem's applicability in complex analysis.

Contribution

It introduces a Szeg"o type result specifically for sequences of powers of finite Blaschke products, expanding the classical theorem's scope.

Findings

Established Szeg"o type results for these sequences.

Connected classical Szeg"o theorem with Blaschke product sequences.

Provided new insights into the structure of model spaces.

Abstract

The classical Szeg\"o theorem can be stated in terms of the sequence of model spaces. In this article, we are interested in the generalization of the Szeg\"o theorem in the case of the sequence of powers of finite Blaschke products.