Szeg\H{o} Limit Theorem for Truncated Toeplitz Operators
Functional Analysis
2024-04-05 v1 Spectral Theory
Abstract
We discuss generalizations of the Szeg\H{o} Limit Theorem to truncated Toeplitz operators. In particular, we consider compressions of Toeplitz operators to an increasing sequence of finite dimensional model spaces. We present two theorems. The first is a new variant of the Szeg\H{o} Limit Theorem in this setting. The second relates to the variant given by Strouse-Timotin-Zarrabi in 2017, and characterizes the sequences for which that result holds.
Cite
@article{arxiv.2404.03087,
title = {Szeg\H{o} Limit Theorem for Truncated Toeplitz Operators},
author = {Nazar Miheisi and Ryan O'Loughlin},
journal= {arXiv preprint arXiv:2404.03087},
year = {2024}
}