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Mathematical Notes

, Volume 106, Issue 3–4, pp 572–576 | Cite as

On Extrapolation of Polynomials with Real Coefficients to the Complex Plane

  • A. S. KochurovEmail author
  • V. M. TikhomirovEmail author
Article
  • 29 Downloads

Abstract

The problem of the greatest possible absolute value of the kth derivative of an algebraic polynomial of order n > k with real coefficients at a given point of the complex plane is considered. It is assumed that the polynomial is bounded by 1 on the interval [-1,1]. It is shown that the solution is attained for the polynomial κ · Tσ, where Tσ is one of the Zolotarev or Chebyshev polynomials and κ is a number.

Keywords

extrapolation alternance Zolotarev polynomial dual problem 

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Notes

Funding

This work was supported by the Russian Foundation for Basic Research under grants 17-01-00649, 16-01-00295, and 17-01-00809.

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Copyright information

© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Lomonosov Moscow State UniversityMoscowRussia

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