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On the constant and step in Jackson’s inequality for best approximations by trigonometric polynomials and by Haar polynomials

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Abstract

Two sharp results for best approximations of periodic functions are established in this paper. We prove the sharpness of the step of the modulus of continuity in Jackson’s inequality with least possible constant for approximations by trigonometric polynomials. We also prove the sharpness of the constants in a Jackson-type inequality for approximations by Haar polynomials in several variables.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    P. A. Andrianov & O. L. Vinogradov

Authors
  1. P. A. Andrianov
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  2. O. L. Vinogradov
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Correspondence to P. A. Andrianov.

Additional information

Original Russian Text © P. A. Andrianov, O. L. Vinogradov, 2016, published in Matematicheskie Zametki, 2016, Vol. 100, No. 3, pp. 323–330.

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Andrianov, P.A., Vinogradov, O.L. On the constant and step in Jackson’s inequality for best approximations by trigonometric polynomials and by Haar polynomials. Math Notes 100, 345–351 (2016). https://doi.org/10.1134/S0001434616090017

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  • DOI: https://doi.org/10.1134/S0001434616090017

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