Hilbert spaces contractively included in the Hardy space of the bidisk

D. Alpay, V. Bolotnikov, A. Dijksma, C. Sadosky

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

We study the reproducing kernel Hilbert spaces Heng hooktop sign (double-struck D2, S) with kernels of the form I - S(z1, Z2 >)S(w1, w2)*/ (1 - z1 w*1)(1 - Z2w*2) where S(z1 ,z2) is a Schur function of two variables z1 ,z2 ∈ double-struck D. They are analogs of the spaces Heng hooktop sign(double-struck D, S) with reproducing kernel (1 -S(z)S(w)*)/(1-zw*) introduced by de Branges and Rovnyak in L. de Branges and J. Rovnyak, Square Summable Power Series Holt, Rinehart and Winston, New York, 1966. We discuss the characterization of Heng hooktop sign(Double-struck D2, S) as a subspace of the Hardy space on the bidisk. The spaces Heng hooktop sign(double-struck D2, S) form a proper subset of the class of the so-called sub-Hardy Hilbert spaces of the bidisk.

Original languageEnglish
Pages (from-to)25-50
Number of pages26
JournalPositivity
Volume5
Issue number1
DOIs
StatePublished - 1 Mar 2001

ASJC Scopus subject areas

  • Analysis
  • Theoretical Computer Science
  • Mathematics (all)

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