Beurling-Lax type theorems and Cuntz relations

B. Schneider; D. Alpay; F. Colombo; I. Sabadini

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arxiv 2108.03630 v1 pith:7DWZOBF2 submitted 2021-08-08 math.CV math.FA

Beurling-Lax type theorems and Cuntz relations

D. Alpay , F. Colombo , I. Sabadini , B. Schneider This is my paper

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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.

Beurling-Lax type theorems and Cuntz relations

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