Weighted Approximation for Jackson-Matsuoka Polynomials on the Sphere

Abstract

We consider the best approximation by Jackson-Matsuoka polynomials in the weighted $L_p$ space on the unit sphere of ${\mathbb{R}}^d$. Using the relation between $K$-functionals and modulus of smoothness on the sphere, we obtain the direct and inverse estimate of approximation by these polynomials for the $h$-spherical harmonics.