Point evaluation and Hardy space on a homogeneous tree

Daniel Alpay, Dan Volok

Research output: Contribution to journalArticlepeer-review

15 Scopus citations

Abstract

We consider stationary multiscale systems as defined by Basseville, Benveniste, Nikoukhah and Willsky. We show that there are deep analogies with the discrete time non stationary setting as developed by the first author, Dewilde and Dym. Following these analogies we define a point evaluation with values in a C*-algebra and the corresponding "Hardy space" in which Cauchy's formula holds. This point evaluation is used to define in this context the counterpart of classical notions such as Blaschke factors.

Original languageEnglish
Pages (from-to)1-22
Number of pages22
JournalIntegral Equations and Operator Theory
Volume53
Issue number1
DOIs
StatePublished - 1 Sep 2005

Keywords

  • Hilbert module
  • Homogeneous tree
  • System realization

ASJC Scopus subject areas

  • Analysis
  • Algebra and Number Theory

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