Some remarks on reproducing kernel krein spaces

Daniel Alpay

Research output: Contribution to journalArticlepeer-review

32 Scopus citations

Abstract

The one-to-one correspondence between positive functions and reproducing kernel Hilbert spaces was extended by L. Schwartz to a (onto, but not one-to-one) correspondence between difference of positive functions and reproducing kernel Krein spaces. After discussing this result, we prove that a matrix valued function K(z, w) symmetric and jointly analytic in z and (Formula Presented)) in a neighborhood of the origin is the reproducing kernel of a reproducing kernel Krein space. We conclude with an example showing that such a function can be the reproducing kernel of two different Krein spaces.

Original languageEnglish
Pages (from-to)1189-1205
Number of pages17
JournalRocky Mountain Journal of Mathematics
Volume21
Issue number4
DOIs
StatePublished - 1 Jan 1991

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