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Approximation of differentiable functions by Fourier-Hermite sums

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Abstract

An asymptotic formula is derived for the divergence of Fourier-Hermite sums from the functions giving rise to them, for functionsf(x) whose r-th derivatives have a modulus of continuity not exceeding a given majorizing modulus of continuity.

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Literature cited

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Authors and Affiliations

  1. Dagestan State University, USSR

    V. A. Abilov & S. A. Agakhanov

Authors
  1. V. A. Abilov
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  2. S. A. Agakhanov
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Additional information

Translated from Matematicheskie Zametki, Vol. 6, No. 1, pp. 35–46, July, 1969.

The authors thank G. I. Natanson for his suggestions which led to the simplification of some of the reasoning.

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Abilov, V.A., Agakhanov, S.A. Approximation of differentiable functions by Fourier-Hermite sums. Mathematical Notes of the Academy of Sciences of the USSR 6, 479–486 (1969). https://doi.org/10.1007/BF01450250

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