Reproducing kernel Hilbert spaces and Mercer theorem

Claudio Carmeli; Ernesto De Vito; Alessandro Toigo

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arXiv · math/0504071

Reproducing kernel Hilbert spaces and Mercer theorem

Claudio Carmeli·Ernesto De Vito·Alessandro Toigo

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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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BibTeX RIS

Claudio Carmeli, Ernesto De Vito, Alessandro Toigo. 2005-04-05. Reproducing kernel Hilbert spaces and Mercer theorem. https://arxiv.org/abs/math/0504071

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