JACKSON TYPE INEQUALITIES FOR DEVIATIONS OF THE RIESZ AVERAGES AND APPLICATIONS TO ESTIMATES OF FUNCTIONALS WITH TWO KNOWN MOMENTS

摘要

We propose a new method for estimating functionals in terms of high order moduli of continuity with explicit constants. This method is used for estimating linear approximation methods by entire functions of exponential type and, in particular, trigonometric polynomials. We prove estimates for deviations of the Riesz averages, which are taken as intermediate approximations. Bibliography: 12 titles.