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Some properties of operators of Abel-Poisson type

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Abstract

We obtain asymptotic estimates for approximations of certain classes of continuous and differentiable functions by operators

$$A_{\gamma , r} (f;x) = \tfrac{1}{\pi }\int_{ - \pi }^\pi {f(x + t)} \left( {\tfrac{1}{2} + \sum\nolimits_{k = 1}^\infty {r^{k^\gamma } cor kt} } \right)dt$$

for γ=1 and 2.

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Authors and Affiliations

  1. Moscow Automotive Transportation Institute, USSR

    V. A. Baskakov

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  1. V. A. Baskakov
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Translated from Matematicheskie Zametki, Vol. 17, No. 2, pp. 169–180, February, 1975.

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Baskakov, V.A. Some properties of operators of Abel-Poisson type. Mathematical Notes of the Academy of Sciences of the USSR 17, 101–107 (1975). https://doi.org/10.1007/BF01161864

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  • DOI: https://doi.org/10.1007/BF01161864

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