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 thisintegral operator gives a complete description of the reproducing kernel, extending Mercer theorem.
Vector Valued Reproducing Kernel Hilbert Spaces Integrable, Functions and Mercer Theorem / C., Carmeli; DE VITO, Ernesto; A., Toigo. - In: ANALYSIS AND APPLICATIONS. - ISSN 0219-5305. - STAMPA. - 4:4(2006), pp. 377-408. [10.1142/S0219530506000838]
Vector Valued Reproducing Kernel Hilbert Spaces Integrable, Functions and Mercer Theorem
DE VITO, Ernesto;
2006
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 thisintegral operator gives a complete description of the reproducing kernel, extending Mercer theorem.
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