Approximation in L2 Sobolev spaces on the 2-sphere by quasi-interpolation

In this article we consider a simple method of radial quasi-interpolation by polynomials on the unit sphere in R-3, and present rates of convergence 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.