Extension of Mercer Theorem for Reproducing Kernel Hilbert Space on Noncompact Sequence of Sets

M. H. Ahmed Yahya

Abstract: In this paper we extend the Mercer theorem to noncompact sequence of Sets, and to establish a functional analysis characterization of the reproducing square kernel Hilbert spaces on general domains.

Keywords: Mercer kernel, Reproducing kernel Hilbert spaces, Nondegenerate Borel measure, Positive Semidefiniteness