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Sampling Theorem in A Reproducing Kernel Hilbert Space

Zhu Jian-li

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Abstract

In this paper,a sampling expansion formula which bases are defined as reproducing kernel function is given by using some special properties of reproducing kernel functions in the Hilbert space at first,then a sampling formula of reproducing kernel function in Hilbert space are derived by using reproducing kernel functions.Meanwhile estimation of error is given.The results play a fundamental role in the problem of numerical approximation and it also convenient to numerical calculations.

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What this paper is about

In this paper,a sampling expansion formula which bases are defined as reproducing kernel function is given by using some special properties of reproducing kernel functions in the Hilbert space at first,then a sampling formula of reproducing kernel function in Hilbert space are derived by using reproducing kernel functions.Meanwhile estimation of error is given.The results play a fundamental role in the problem of numerical approximation and it also convenient to numerical calculations.

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Available abstract

In this paper,a sampling expansion formula which bases are defined as reproducing kernel function is given by using some special properties of reproducing kernel functions in the Hilbert space at first,then a sampling formula of reproducing kernel function in Hilbert space are derived by using reproducing kernel functions.Meanwhile estimation of error is given.The results play a fundamental role in the problem of numerical approximation and it also convenient to numerical calculations.

Key concepts: Reproducing kernel Hilbert space, Representer theorem, Mathematics, Kernel (algebra), Hilbert space, Kernel embedding of distributions, Sampling (signal processing), Applied mathematics

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