Polyharmonic approximation on the sphere (Q623351)

The author develops an approximation scheme [cf. \textit{S. Hubbert} and \textit{T. M. Morton}, J. Approximation Theory 129, No. 1, 58--77 (2004; Zbl 1065.41004)] delivering novel error estimates for a robust family of spherical basis functions: the polyharmonic kernels (which are fundamental solutions for certain elementary partial differential operators). This is the family of Green's functions of iterated and perturbed Laplace-Beltrami operators. The development of the scheme presented here is based on replacing the kernel in an integral identity by a linear combination of scattered rotations of the kernel [cf. \textit{R. DeVore} and \textit{A. Ron}, Trans. Am. Math. Soc. 362, No. 12, 6205--6229 (2010; Zbl 1215.41004)].