On On the approximation of functions by Jacobi – Dunkl expansion in the weighted space 𝕃 2 ( α , β )

Abstract

UDC 517.5 We prove some new estimates useful in applications for the approximation of certain classes of functions characterized by the generalized continuity modulus from the space 𝕃 2 ( α , β ) by partial sums of the Jacobi – Dunkl series. For this purpose, we use the generalized Jacobi – Dunkl translation operator obtained by Vinogradov in the monograph [Theory of approximation of functions of real variable, Fizmatgiz, Moscow (1960) (in Russian)].