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 Mat. Zametki: Year: Volume: Issue: Page: Find

 Mat. Zametki, 2012, Volume 91, Issue 5, Pages 761–772 (Mi mz8759)

Approximation to the Function $z^{\alpha}$ by Rational Fractions in a Domain with Zero External Angle

A. A. Pekarskii

Belarusian State Technological University

Abstract: Rational approximations to the function $z^{\alpha}$, $\alpha\in\mathbb{R}\setminus\mathbb{Z}$, were studied by Newman, Gonchar, Bulanov, Vyacheslavov, Andersson, Stahl, and others. The present paper deals with the order of best rational approximations to this function in a domain with zero external angle and vertex at the point $z=0$. In particular, the obtained results show that the conditions imposed on the boundary of the domain in the Jackson-type inequality proved by the author in 2001 for the best rational approximations in Smirnov spaces cannot be weakened significantly.

Keywords: best uniform rational approximation, polynomial approximation, Smirnov space, analytic function, rational function, rectifiable Jordan boundary, Lavrentiev curve

DOI: https://doi.org/10.4213/mzm8759

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English version:
Mathematical Notes, 2012, 91:5, 714–724

Bibliographic databases:

UDC: 517.53
Revised: 18.03.2011

Citation: A. A. Pekarskii, “Approximation to the Function $z^{\alpha}$ by Rational Fractions in a Domain with Zero External Angle”, Mat. Zametki, 91:5 (2012), 761–772; Math. Notes, 91:5 (2012), 714–724

Citation in format AMSBIB
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• http://mi.mathnet.ru/eng/mz8759
• https://doi.org/10.4213/mzm8759
• http://mi.mathnet.ru/eng/mz/v91/i5/p761

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This publication is cited in the following articles:
1. G. Wang, J. Li, “Approximations of fuzzy numbers by step type fuzzy numbers”, Fuzzy Sets and Systems, 310 (2017), 47–59
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