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Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree

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Abstract

We construct a new class of positive definite and compactly supported radial functions which consist of a univariate polynomial within their support. For given smoothness and space dimension it is proved that they are of minimal degree and unique up to a constant factor. Finally, we establish connections between already known functions of this kind.

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Communicated by J.C. Mason

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Wendland, H. Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. Adv Comput Math 4, 389–396 (1995). https://doi.org/10.1007/BF02123482

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  • DOI: https://doi.org/10.1007/BF02123482

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