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Approximation estimates for convolution classes in terms of the second modulus of continuity

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Abstract

We establish the best approximation estimates for certain convolutions whose kernels are entire functions of exponential type in terms of the second modulus of continuity. The Jackson-type inequalities for even-order derivatives are particular cases of our estimates.

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References

  1. Zhuk V. V., Approximation of Periodic Functions [in Russian], Leningrad Univ., Leningrad (1982).

    Google Scholar 

  2. Zhuk V. V., “Some sharp inequalities between best approximations and moduli of continuity,” Siberian Math. J., 12, No. 6, 924–930 (1971).

    Article  MathSciNet  Google Scholar 

  3. Ligun A. A., “Exact constants of approximation for differentiable periodic functions,” Math. Notes, 14, No. 1, 563–569 (1973).

    Article  Google Scholar 

  4. Korneĭchuk N. P., Exact Constants in Approximation Theory [in Russian], Nauka, Moscow (1987).

    Google Scholar 

  5. Gromov A. Yu., “On exact constants in approximation by entire functions of differentiable functions,” Studies on Modern Summability Problems and Approximations of Functions and Some of Their Applications. Dnepropetrovsk. Vol.7, pp. 17–21 (1976).

    MathSciNet  Google Scholar 

  6. Vinogradov O. L., “Sharp Jackson-type inequalities for approximations of classes of convolutions by entire functions of exponential type,” St. Petersburg Math. J., 17, No. 4, 593–633 (2006).

    Article  MATH  MathSciNet  Google Scholar 

  7. Vinogradov O. L. and Zhuk V. V., “Estimates of functionals by the second modulus of continuity of even derivatives,” Zap. Nauchn. Sem. POMI, 416, 70–90 (2013).

    Google Scholar 

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

    Google Scholar 

  9. Titchmarsh E. C., Introduction to the Theory of Fourier Integrals, Clarendon Press, Oxford (1937).

    Google Scholar 

  10. Zhuk V. V. and Kuzyutin V. F., Approximation of Functions and Numerical Integration [in Russian], St. Petersburg Univ., St. Petersburg (1995).

    Google Scholar 

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Authors and Affiliations

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

    O. L. Vinogradov

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  1. O. L. Vinogradov
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Correspondence to O. L. Vinogradov.

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Original Russian Text Copyright © 2014 Vinogradov O.L.

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 3, pp. 494–508, May–June, 2014.

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Vinogradov, O.L. Approximation estimates for convolution classes in terms of the second modulus of continuity. Sib Math J 55, 402–414 (2014). https://doi.org/10.1134/S0037446614030021

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  • DOI: https://doi.org/10.1134/S0037446614030021

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