On Modulus of Smoothness of Functions Given on Compact Groups

Abstract

The connection between structural and constructive characterization of a function is one of the most important problems of approximation theory and this relations is given by Jackson type theorems. The structural properties of functions, i.e., the modulus of smoothness can be given by different methods. In this article we define different moduli of smoothness of order k for functions and study the relations between these moduli of smoothness and give some unsolved problems on equivalence of these definitions. Also we will prove some Jackson type theorems on compact groups.