Title

Some Reproducing Kernel Spaces of Continuous Functions

Document Type

Article

Publication Date

1991

Abstract

By a result of L. Schwartz, a symmetric function is the reproducing kernel of a reproducing kernel Krein space if and only if it can be written as a difference of two positive functions; it seems, in general, difficult to check this last criteria. In the present study we show that a n × n valued symmetric function K(t, s) of class b^3 for t, s ϵ (a, b) is the reproducing kernel of a reproducing kernel Krein space of continuous functions. We first obtain a more general result when the symmetry hypothesis is removed and the Krein space is replaced by a pair of Hilbert spaces in duality with respect to a sesquilinear form.

Comments

This article was originally published in Journal of Mathematical Analysis and Applications, volume 160, in 1991. DOI: 10.1016/0022-247X(91)90315-Q

Peer Reviewed

1

Copyright

Elsevier