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Sharp estimates for the convergence rate of Fourier—Bessel series

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Abstract

Sharp estimates are derived for the convergence rate of Fourier series in terms of Bessel functions of the first kind for some classes of functions characterized by a generalized modulus of continuity. The Kolmogorov N-width of these classes of functions are also estimated.

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References

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Authors and Affiliations

  1. Dagestan State University, ul. Gadzhieva 43a, Makhachkala, 367025, Russia

    V. A. Abilov

  2. Dagestan State Technical University, pr. Shamilya 70, Makhachkala, 367015, Russia

    F. V. Abilova

  3. Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119333, Russia

    M. K. Kerimov

Authors
  1. V. A. Abilov
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  2. F. V. Abilova
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  3. M. K. Kerimov
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Correspondence to V. A. Abilov.

Additional information

Original Russian Text © V.A. Abilov, F.V. Abilova, M.K. Kerimov, 2015, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2015, Vol. 55, No. 6, pp. 917–927.

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Abilov, V.A., Abilova, F.V. & Kerimov, M.K. Sharp estimates for the convergence rate of Fourier—Bessel series. Comput. Math. and Math. Phys. 55, 907–916 (2015). https://doi.org/10.1134/S0965542515060020

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  • DOI: https://doi.org/10.1134/S0965542515060020

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