Abstract
The result obtained in this paper allows one to identify the approximate convergence at a point (or its absence) of the values of the Whittaker operators: The only requirement on the function to be approximated is its continuity on . The information about can be reduced to its values at the nodes lying in a neighbourhood of the point at which the approximation properties are actually under consideration.A test for the uniform convergence of these operators on compact subsets of is also obtained for continuous functions, which is similar to Privalov's criterion of the convergence of the Lagrange-Chebyshev interpolation polynomials and trigonometric polynomials.Bibliography: 32 titles.
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