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. (C) 2021 Elsevier Inc. All rights reserved.
de Branges-Rovnyak spacesCuntz relationsRational functionsBeurling-Lax theoremBackward-shift operatorStructure theoremsINTERPOLATIONREPRESENTATIONSREALIZATIONALGEBRASSPACES
NSTL
Elsevier
