We study Sobolev type estimates for the approximation order resulting from using strictly positive definite kernels to do interpolation on the n-sphere. The interpolation knots are scattered. Our… (More)

We investigate the construction of cubature formulas for the unit sphere in IR n that have almost equal weights. The corresponding knots are taken from equidistributed point sets on the sphere. The… (More)

We discuss order of convergence for subdivision algorithms, in the scalar-valued and the vector-valued case. In order to find the generic order, the usual definition of convergence order is extended,… (More)

This paper aims at providing a self-contained introduction to notions and results connected with the L 2-approximation power of nitely generated shift-invariant spaces (FSI spaces) S L 2 (R d). Here,… (More)

A new class of differential operators on the simplex is introduced, which define weighted Sobolev normsandwhoseeigenfunctions are orthogonal polynomialswith respect to Jacobiweights.Theseoperators… (More)

In this paper we introduce a class of Bernstein–Durrmeyer operators with respect to an arbitrary measure ρ on the d-dimensional simplex, and a class of more general polynomial integral operators with… (More)