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Sharp Inequalities for Seminorms Defined on Spaces of Periodic Functions

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We present a polynomial approximation method for realizing modified Landau–Kolmogorov type inequalities with small order derivatives. Bibliography: 6 titles.

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References

  1. V. V. Zhuk, “Some sharp inequalities between uniform best approximations of periodic functions,” Sov. Math., Dokl. 12, 1633-1636 (1971).

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  2. V. V. Zhuk, “Some inequalities between best approximations of periodic functions” [in Russian] Izv. Vyssh. Uchebn. Zaved., Mat. No. 9, 18–26 (1973).

  3. V. V. Zhuk, Approximation of Periodic Functions [in Russian], Leningr. Univ. Press, Leningr. (1982).

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  4. O. L. Vinogradov and V. V. Zhuk, “Extensions to the Jackson-type and Landau-Kolmogorov-type sharp inequalities for derivatives of low order,” Vestn. St. Petersbg. Univ., Math. 36, No. 4, 8-16 (2003).

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  5. V. V. Zhuk and G. I. Natanson, Trigonometric Fourier Series and Elements of Approximation Theory [in Russian], Leningr. State Univ. Press, Leningr. (1983).

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  6. N. I. Akhiezer, Lectures on Approximation Theory [in Russian], Nauka, Moscow (1965).

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Correspondence to V. V. Zhuk.

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Translated from Problemy Matematicheskogo Analiza 90, January 2018, pp. 55-62.

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Zhuk, V.V. Sharp Inequalities for Seminorms Defined on Spaces of Periodic Functions. J Math Sci 228, 662–671 (2018). https://doi.org/10.1007/s10958-017-3654-3

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  • DOI: https://doi.org/10.1007/s10958-017-3654-3

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