A Theorem on Reproducing Kernel Hilbert Spaces of Pairs

Authors

Daniel Alpay, Chapman UniversityFollow

Document Type

Article

Publication Date

1992

Abstract

In this paper we study reproducing kernel Hilbert and Banach spaces of pairs. These are a generalization of reproducing kernel Krein spaces and, roughly speaking, consist of pairs of Hilbert (or Banach) spaces of functions in duality with respect to a sesquilinear form and admitting a left and right reproducing kernel. We first investigate some properties of these spaces of pairs. It is then proved that to every function K(z, ω) analytic in z and ω* 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, ω) and right reproducing kernel K(ω, z)*.

Comments

This article was originally published in Rocky Mountain Journal of Mathematics, volume22, in 1992 DOI:10.1216/rmjm/1181072652

Recommended Citation

D. Alpay. A theorem on reproducing kernel Hilbert spaces of pairs. Rocky Mountain J. Math. 22 (1992), no. 4, 1243-1258.

Peer Reviewed

1

Copyright

Rocky Mountain Mathematics Consortium