Szeg\H{o} and Widom theorems for finite codimensional subalgebras of a class of uniform algebras

TL;DR

This paper extends Szeg\

Contribution

It develops versions of Szeg\

Findings

Szeg\

Widom's theorem adapted to finite codimensional subalgebras

Representation of these algebras on reproducing kernel Hilbert spaces

Abstract

We establish versions of Szeg\H{o}'s distance formula and Widom's theorem on invertibility of (a family of) Toeplitz operators in a class of finite codimension subalgebras of uniform algebras, obtained by imposing a finite number of linear constraints. Each such algebra is naturally represented on a family of reproducing kernel Hilbert spaces, which play a central role in the proofs.