On a new class of structured reproducing kernel spaces

D. Alpay, H. Dym

Research output: Contribution to journalArticlepeer-review

49 Scopus citations

Abstract

A class of reproducing kernel spaces with reproducing kernels of the form Kω(λ) = (J - Θ(λ)JΘ(ω)*)/ρω (λ) with pω(λ) = a(λ)a(ω)* is characterized in terms of invariance under a pair of generalized shift operators and a structural identity. This incorporates a characterization of de Branges for the “line” case and a later analogue due to Ball for the “circle” case, as well as many other possibilities, by specializing the choice of ρ. These results also permit the extension of some earlier characterizations by the authors of finite dimensional spaces with reproducing kernels of the form given above to the infinite dimensional case. The non-Hermitian case is also considered.

Original languageEnglish
Pages (from-to)1-28
Number of pages28
JournalJournal of Functional Analysis
Volume111
Issue number1
DOIs
StatePublished - 1 Jan 1993

ASJC Scopus subject areas

  • Analysis

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