Piecewise polynomial, positive definite and compactly supported radial functions of minimal degree (Q1906079)

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.