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 re producing kernel. Moreover, for p = 2 we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending Mercer theorem.
Vector Valued Reproducing Kernel Hilbert Spaces Integrable, Functions and Mercer Theorem
CARMELI, CLAUDIO;DE VITO, ERNESTO;TOIGO, ALESSANDRO
2006-01-01
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 re producing kernel. Moreover, for p = 2 we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel, extending Mercer theorem.
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