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.
Recommended Citation
D. Alpay, Some remarks on reproducing kernel Krein spaces, The Rocky Mountain Journal of Mathematics, vol. 21 (1991) 1189-1205.
Peer Reviewed
1
Copyright
Rocky Mountain Mathematics Consortium
Comments
This article was originally published in Rocky Mountain Journal of Mathematics, volume 21, in 1991. DOI:10.1216/rmjm/1181072903