Properties of generators of quasi-interpolation operators of high approximation orders in spaces of polyharmonic splines

摘要

We have presented in Bozzini et al. (2011) a procedure in spaces of m-harmonic splines in R~d that starts from a simple generator φ_0 and recursively defines generators φ_1, φ_2, …, φ_(m-1) with corresponding quasi-interpolation operators reproducing polynomials of degrees 3, 5, …, 2m-1 respectively. In this paper we study the properties of generators φ_j, and we prove that these new generators are positive definite functions, and are scaling functions whenever φ_0 has those properties. Moreover φ_0 and φ_j generate the same multiresolution analysis.Weshow that it is possible to define a convergent subdivision scheme, and to provide in this way a fast computation of the quasi-interpolant.