Approximations on compact symmetric spaces of rank 1

Abstract

On an arbitrary Riemannian symmetric space of rank 1 the Nikol'skii classes are defined by considering differences along geodesics. These spaces are described in terms of the best approximations by polynomials in spherical harmonics on , that is, by linear combinations of the eigenfunctions of the Laplace-Beltrami operator on . The results of Nikol'skii and Lizorkin on the approximation of functions on the sphere are generalized.