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Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree. (English) Zbl 0838.41014
The author constructs a class of positive definite and compactly supported radial functions of even order of smoothness, which are defined – within their supports – by a single univariate polynomial. For given space dimension and smoothness, it is shown that these functions have minimal degree, and that they are uniquely determined up to a constant factor. Finally, connections are made to other compactly supported positive definite radial functions, namely the so-called Wu’s functions and Euclid’s hats.
Reviewer: E.Quak (Schwerte)

41A30 Approximation by other special function classes
41A05 Interpolation in approximation theory
41A63 Multidimensional problems (should also be assigned at least one other classification number from Section 41-XX)
41A15 Spline approximation
65D07 Numerical computation using splines
65D10 Numerical smoothing, curve fitting
Full Text: DOI
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