A theorem on reproducing kernel hilbert spaces of pairs

Daniel Alpay

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

In this paper we study reproducing kernel Hilbert and Banacli spaces of pairs. These are a generalization of reproducing kernel Hilbert spaces and, roughly speaking, consist of pairs of Hilbert (or Banaeh) spaces of functions in duality with respect to a sesquilinear form and admitting a left and a right reproducing kernel. We first investigate some properties of these spaces of pairs. It is then proved that to every function K(z,w) analytic in z and w* there is a neighborhood of the origin that can be associated with a reproducing kernel Hilbert space of pairs with left reproducing kernel K(z,w) and right reproducing kernel K(w, z)*.

Original languageEnglish
Pages (from-to)1243-1258
Number of pages16
JournalRocky Mountain Journal of Mathematics
Volume22
Issue number4
DOIs
StatePublished - 1 Sep 1992

ASJC Scopus subject areas

  • General Mathematics

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