Abstract
We provide criteria for positive definiteness of radial functions with compact support. Based on these criteria we will produce a series of positive definite and compactly supported radial functions, which will be very useful in applications. The simplest ones arecut-off polynomials, which consist of a single polynomial piece on [0, 1] and vanish on [1, ∞). More precisely, for any given dimensionn and prescribedC k smoothness, there is a function inC k(ℝn), which is a positive definite radial function with compact support and is a cut-off polynomial as a function of Euclidean distance. Another example is derived from odd-degreeB-splines.
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Communicated by J.C. Mason
The work was done during the author’s visit to Göttingen with support of a DAAD-Wong fellowship.
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Wu, Z. Compactly supported positive definite radial functions. Adv Comput Math 4, 283–292 (1995). https://doi.org/10.1007/BF03177517
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DOI: https://doi.org/10.1007/BF03177517