Minimal degree univariate piecewise polynomials with prescribed Sobolev regularity (Q657432)

An even compactly supported piecewise polynomial whose Fourier transform satisfies some conditions is constructed. The degree of it is shown to be minimal and is strictly less than that of Wendland's function. This shows that, for \(\kappa>2\), Wendland's piecewise polynomial \(\phi_{1,\kappa-1}\) is not of minimal degree if one places no restrictions on the number of pieces.