Reproducing kernel Hilbert spaces and Mercer theorem

2005/04/05 by Claudio Carmeli, Carmeli, Claudio, Ernesto De Vito +3 · 1 citation
Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #math-ph #math.FA #math.MP

paper · pdf · doi:10.48550/arxiv.math/0504071

30 pages, Latex2e

arxiv created 2005/04/05 · arxiv updated 2009/12/01

Abstract

We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p=2 we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel.

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