A Szeg\H{o} Limit Theorem for Radially-Compressed Toeplitz Operators

TL;DR

This paper establishes Szeg\

Contribution

It introduces Szeg\

Findings

Eigenvalue density formulas for compressed Toeplitz operators

Limit theorems in Reproducing Kernel Hilbert Spaces on discs

Applications to Bergman and Segal-Bargmann-Fock spaces

Abstract

We obtain Szeg\H{o}-type Limit Theorems in the setting of Reproducing Kernel Hilbert Spaces on discs in $\mathbb{C}$. From this, we derive a formula for the density of the eigenvalues of compressions of Toeplitz operators. Examples for the Bergman and Segal-Bargmann-Fock space are also presented.