Generalized gegenbauer shift and some problems of the theory of approximation of functions on the metric of L2,?

Abstract

In this paper we consider some problems of the theory of approximation of functions on interval [0, ?) in the metric of L2,? with weight sh2?x. The modulus of continuity used in those problems is constructed with the help of generalized Gegenbauer shift operator. The direct Jakson type theorems are proved. The function spaces of Nikolski-Besov type associated with Gegenbauer differential operator D? are introduced and their descriptions in terms of best approximations are obtained. © 2015, Institute of Mathematics and Mechanics, National Academy of Sciences of Azerbaijan. All rights reserved.