Approximation inL 2 Sobolev spaces on the 2-sphere by quasi-interpolation

Abstract

In this article we consider a simple method of radial quasi-interpolation by polynomials on the unit sphere in ℝ3, and present rates of covergence for this method in Sobolev spaces of square integrable functions. We write the discrete Fourier series as a quasi-interpolant and hence obtain convergence rates, in the aforementioned Sobolev spaces, for the discrete Fourier projection. We also discuss some typical practical examples used in the context of spherical wavelets.