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

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