A criterion for the uniform convergence of sinc-approximations on a segment

Abstract

In this paper we obtain a criterion for the uniform convergence inside the interval (0, π) of values of E. T. Whittaker operators $$ L_n (f,x) = \sum\limits_{k = 0}^n {\frac{{sin(nx - k\pi )}} {{nx - k\pi }}f\left( {\frac{{k\pi }} {n}} \right)} $$ for continuous functions. This criterion is similar to that of A. A. Privalov for the convergence of interpolation Lagrange-Chebyshev polynomials and trigonometric ones.