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On the Convergence of Generalizations of the Sinc Approximations on the Privalov–Chanturia Class

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Abstract

We establish some condition in terms of the left or right modulus of continuity and the negative or positive modulus of variation of a function \(f \) respectively that is sufficient for uniform approximation of \(f \) by the values of the function interpolation operators constructed from the solutions of the Cauchy problem with a linear differential expression of the second order inside an interval. These operators are some generalization of the classical sinc approximations used in the Whittaker–Kotelnikov–Shannon Sampling Theorem. We show also that this condition is sufficient for the uniform convergence over the entire segment of some modification of the function interpolation operator, which allows us to eliminate the Gibbs phenomenon near the endpoints of the segment.

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Authors and Affiliations

  1. Chernyshevskii Saratov State University, Saratov, 410012, Russia

    A. Yu. Trynin

  2. Moscow Center for Fundamental and Applied Mathematics, Moscow State University, Moscow, 119991, Russia

    A. Yu. Trynin

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Translated by L.B. Vertgeim

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Trynin, A.Y. On the Convergence of Generalizations of the Sinc Approximations on the Privalov–Chanturia Class. J. Appl. Ind. Math. 15, 531–542 (2021). https://doi.org/10.1134/S1990478921030145

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  • DOI: https://doi.org/10.1134/S1990478921030145

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