Beurling-Lax type theorems and Cuntz relations

Daniel Alpay, Fabrizio Colombo, Irene Sabadini, Baruch Schneider

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)152-212
Number of pages61
JournalLinear Algebra and Its Applications
StatePublished - 15 Jan 2022
Externally publishedYes


  • Backward-shift operator
  • Beurling-Lax theorem
  • Cuntz relations
  • Rational functions
  • Structure theorems
  • de Branges-Rovnyak spaces

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Numerical Analysis
  • Geometry and Topology
  • Discrete Mathematics and Combinatorics


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