Schur multipliers and de Branges-Rovnyak spaces: The multiscale case

Daniel Alpay, Aad Dijksma, Dan Volok

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We consider bounded linear operators acting on the 2 space indexed by the nodes of a homogeneous tree. Using the Cuntz relations between the primitive shifts on the tree, we generalize the notion of the single-scale time-varying point evaluation and introduce the corresponding reproducing kernel Hilbert space in which Cauchy's formula holds. These notions are then used in the study of the Schur multipliers and of the associated de Branges-Rovnyak spaces. As an application we obtain realization of Schur multipliers as transfer operators of multiscale input-state-output systems.

Original languageEnglish
Pages (from-to)87-118
Number of pages32
JournalJournal of Operator Theory
Issue number1
StatePublished - 1 Jan 2009


  • Homogeneous tree
  • Non-commutative power series
  • System realization

ASJC Scopus subject areas

  • Algebra and Number Theory


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