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Constants in Jackson Type Inequalities for the Best Approximation of Periodic Functions Such that Some of Their Fourier Coefficients Vanish

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We consider the class of continuous 2π-periodic functions such that some of their Fourier coefficients vanish. For such functions we study constants in a generalized Jackson theorem providing an estimate for the best approximation by trigonometric polynomials with the help of the moduli of continuity of an arbitrary order.

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References

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Authors and Affiliations

  1. St. Petersburg State University, 28, Universitetskii pr., St. Petersburg, 198504, Russia

    V. V. Zhuk & V. M. Bure

Authors
  1. V. V. Zhuk
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  2. V. M. Bure
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Correspondence to V. V. Zhuk.

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Dedicated to Nina Nikolaevna Uraltseva

Translated from Problemy Matematicheskogo Analiza 78, January 2015, pp. 95-102.

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Zhuk, V.V., Bure, V.M. Constants in Jackson Type Inequalities for the Best Approximation of Periodic Functions Such that Some of Their Fourier Coefficients Vanish. J Math Sci 207, 218–225 (2015). https://doi.org/10.1007/s10958-015-2367-8

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  • DOI: https://doi.org/10.1007/s10958-015-2367-8

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