Reproducing kernel Hilbert spaces and Mercer theorem

Details Reproducing kernel Hilbert spaces and Mercer theorem Reproducing kernel Hilbert spaces and Mercer theorem

2005-04-05

arxiv.org/abs/math/0504071v1

Mathematics

Functional Analysis

30 pages, Latex2e

Scientific paper

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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