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

In this article we consider a simple method of radial quasi-interpolation b y polynomials on the unit sphere in R-3, and present rates of convergence f or this method in Sobolev spaces of square integrable functions. We write t he discrete Fourier series as a quasi-interpolant and hence obtain converge nce rates, in the aforementioned Sobolev spaces, for the discrete Fourier p rojection. we also discuss some typical practical examples used in the cont ext of spherical wavelets.