Geodesic
On Extrapolation of Polynomials with Real Coefficients to the Complex Plane
Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 543-548

Voir la notice de l'article provenant de la source Math-Net.Ru

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.
Mots-clés : extrapolation, alternance, Zolotarev polynomial
Keywords: dual problem. 
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     author = {A. S. Kochurov and V. M. Tikhomirov},
     title = {On {Extrapolation} of {Polynomials} with {Real} {Coefficients} to the {Complex} {Plane}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {543--548},
     publisher = {mathdoc},
     volume = {106},
     number = {4},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a5/}
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A. S. Kochurov; V. M. Tikhomirov. On Extrapolation of Polynomials with Real Coefficients to the Complex Plane. Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 543-548. http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a5/