Approximation by Spherical de la Vallee-Poussin Mean Operators
The classical de la Vallee-Poussin mean operators have played important roles in approximation theory and harmonic analysis. This paper considers two kinds of spherical de la Vallee-Poussin mean operators. The first class is constructed by the convolution with a generalizing de la Vallee-Poussin kernel on the unit sphere, and the second one proposed in this paper is the convolution's discrete version on some regular grid points of the unit sphere. The errors, these operators approximating target functions in Sobolev space, are estimated. Furthermore, the upper bound and the convergence of the discrete type operators are discussed.
approximation de la vallee-poussin mean sphere filter