RUS  ENG
Full version
JOURNALS // Matematicheskie Zametki // Archive

Mat. Zametki, 2019 Volume 106, Issue 4, Pages 543–548 (Mi mzm12260)

This article is cited in 1 paper

On Extrapolation of Polynomials with Real Coefficients to the Complex Plane

A. S. Kochurov, V. M. Tikhomirov

Lomonosov Moscow State University

Abstract: The problem of the greatest possible absolute value of the $k$th 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 $\kappa\cdot T_\sigma$, where $T_\sigma$ is one of the Zolotarev or Chebyshev polynomials and $\kappa$ is a number.

Keywords: extrapolation, alternance, Zolotarev polynomial, dual problem.

UDC: 517

Received: 11.12.2018
Revised: 15.02.2019

DOI: 10.4213/mzm12260


 English version:
Mathematical Notes, 2019, 106:4, 572–576

Bibliographic databases:


© Steklov Math. Inst. of RAS, 2025