Approximation in \(L_2\) Sobolev spaces on the 2-sphere by quasi-interpolation (Q5939345)

The authors consider radial quasi-interpolation by polynomials on the unit sphere in \(\mathbb{R}^3\), and present error estimates for quasi-interpolation in Sobolev spaces. Using equiangular grid points, a discrete Fourier transform on the sphere is studied. The authors show how the discrete Fourier series is a special case of the general framework, and give error bounds for the discrete Fourier projection in Sobolev spaces. Some applications in spherical wavelet analysis are discussed too.