Some Remarks on Reproducing Kernel Krein Spaces

Document Type

Article

Publication Date

1991

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 matrix value function K(z,ω) symmetric and jointly analytic in z and ω 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.

Comments

This article was originally published in Rocky Mountain Journal of Mathematics, volume 21, in 1991. DOI:10.1216/rmjm/1181072903

Peer Reviewed

1

Copyright

Rocky Mountain Mathematics Consortium

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