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Sharp estimates of best approximations in terms of holomorphic functions of weierstrass-type operators

Journal of Mathematical Sciences volume 193, pages 8–31 (2013)Cite this article

Estimates of the form

$$ {A_{\sigma }}{(f)_P}\leq KP\left( {\varPhi \left( \mathcal{W} \right)f} \right), $$

where W is a kernel of a special type summable on \( \mathbb{R} \), a function Φ is holomorphic in a neighborhood of the spectrum of W, and A σ(f ) P is the best approximation of a function f by entire functions of exponential type not greater than σ with respect to a seminorm P, are established. In some cases, for the uniform and integral norms the least possible constant K is found. The estimates are obtained by linear approximation methods. Bibliography: 13 titles.

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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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Translated from Zapiski Nauchnykh Seminarov POMI, V0l. 404, 2012, pp. 18–60.

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Vinogradov, O.L. Sharp estimates of best approximations in terms of holomorphic functions of weierstrass-type operators. J Math Sci 193, 8–31 (2013). https://doi.org/10.1007/s10958-013-1429-z

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  • DOI: https://doi.org/10.1007/s10958-013-1429-z

Keywords

  • Approximation Method
  • Holomorphic Function
  • Linear Approximation
  • Entire Function
  • Exponential Type