Mercer theorem for RKHS on noncompact sets. (English) Zbl 1094.46021

Summary: Reproducing kernel Hilbert spaces are an important family of function spaces and play useful roles in various branches of analysis and applications including the kernel machine learning. When the domain of definition is compact, they can be characterized as the image of the square root of an integral operator, by means of the Mercer theorem. The purpose of this paper is to extend the Mercer theorem to noncompact domains, and to establish a functional analysis characterization of the reproducing kernel Hilbert spaces on general domains.


46E22 Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces)
28C15 Set functions and measures on topological spaces (regularity of measures, etc.)
68T05 Learning and adaptive systems in artificial intelligence
68Q32 Computational learning theory
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