APPROXIMATION OF FUNCTIONS ON THE SPHERE
Sergei Mikhailovich Nikol'skii, П. И. Лизоркин · Mathematics of the USSR-Izvestiya · 1988
The authors consider classes of functions on a sphere , whose smoothness is determined by the properties of differences along geodesics (duly averaged) in the metric of . An integral representation of a function is obtained in terms of the differences mentioned. On this basis direct and inverse theorems on approximation of functions be polynomials in spherical harmonics are established. These theorems completely characterize the class . Bibliography: 9 titles.