Abstract:
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.
Keywords:cardinal function, sinc approximation, Lagrange interpolation, convergence; criterion of the uniform convergence, cardinal function, approximation, interpolation process.
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