Beurling-Lax type theorems and Cuntz relations
Complex Variables
2022-02-01 v1 Functional Analysis
Abstract
We prove various Beurling-Lax type theorems, when the classical backward-shift operator is replaced by a general resolvent operator associated with a rational function. We also study connections to the Cuntz relations. An important tool is a new representation result for analytic functions, in terms of composition and multiplication operators associated with a given rational function. Applications to the theory of de Branges-Rovnyak spaces, also in the indefinite metric setting, are given.
Cite
@article{arxiv.2108.03630,
title = {Beurling-Lax type theorems and Cuntz relations},
author = {D. Alpay and F. Colombo and I. Sabadini and B. Schneider},
journal= {arXiv preprint arXiv:2108.03630},
year = {2022}
}