Beurling-Lax Type Theorems and Cuntz Relations

Authors

Daniel Alpay, Chapman UniversityFollow
Fabrizio Colombo, Politecnico di Milano
Irene Sabadini, Politecnico di Milano
Baruch Schneider, University of Ostrava

Document Type

Article

Publication Date

8-8-2021

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.

Comments

This is the originally-submitted version of an article that later underwent peer review and was accepted for publication in Linear Algebra and Its Applications, volume 633, in 2021. The definitive publisher-authenticated version may differ and is available online at https://doi.org/10.1016/j.laa.2021.10.008.

Recommended Citation

Citation for published, peer-reviewed article:

D. Alpay, F. Colombo, I. Sabadini, and B. Schneider. Beurling-Lax type theorems and Cuntz relations. Linear Algebra and Its Applications, 633:152-212, 2021. https://doi.org/10.1016/j.laa.2021.10.008

Copyright

Elsevier