Borodin-Okounkov and Szeg\"o for Toeplitz operators on model spaces

TL;DR

This paper extends classical results like the Borodin-Okounkov formula and Szeg"o limit theorem to the setting of Toeplitz operators compressed to finite-dimensional model spaces, providing new insights into their determinants.

Contribution

It introduces analogues of the Borodin-Okounkov formula and Szeg"o limit theorem specifically for Toeplitz operators on model spaces, a novel extension of these classical results.

Findings

Derived formulas for determinants of compressed Toeplitz operators on model spaces.

Established analogues of classical theorems in a new operator setting.

Provided mathematical tools for analyzing Toeplitz operators in finite-dimensional contexts.

Abstract

We consider the determinants of compressions of Toeplitz operators to finite-dimensional model spaces and establish analogues of the Borodin-Okounkov formula and the strong Szeg\"o limit theorem in this setting.