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Beurling-Lax Type Theorems And Cuntz Relations, Daniel Alpay, Fabrizio Colombo, Irene Sabadini, Baruch Schneider
Beurling-Lax Type Theorems And Cuntz Relations, Daniel Alpay, Fabrizio Colombo, Irene Sabadini, Baruch Schneider
Mathematics, Physics, and Computer Science Faculty Articles and Research
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.