Geodesic
Reproducing Kernel Hilbert Spaces Associated with Kernels on Topological Spaces
Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 89-91

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We analyze reproducing kernel Hilbert spaces of positive definite kernels on a topological space $X$ being either first countable or locally compact. The results include versions of Mercer's theorem and theorems on the embedding of these spaces into spaces of continuous and square integrable functions.
Keywords: reproducing kernel Hilbert spaces, positive definite kernels, Mercer's theory. 
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     author = {V. A. Menegatto and J. C. Ferreira},
     title = {Reproducing {Kernel} {Hilbert} {Spaces} {Associated} with {Kernels} on {Topological} {Spaces}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
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V. A. Menegatto; J. C. Ferreira. Reproducing Kernel Hilbert Spaces Associated with Kernels on Topological Spaces. Funkcionalʹnyj analiz i ego priloženiâ, Tome 46 (2012) no. 2, pp. 89-91. http://geodesic.mathdoc.fr/item/FAA_2012_46_2_a8/