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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     title = {On {Extrapolation} of {Polynomials} with {Real} {Coefficients} to the {Complex} {Plane}},
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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/

[1] V. M. Tikhomirov, Nekotorye voprosy teorii priblizhenii, Izd-vo Mosk. un-ta, M., 1976 | MR

[2] N. I. Akhiezer, Lektsii po teorii approksimatsii, Nauka, M., 1965 | MR | Zbl

[3] G. G. Magaril-Ilyaev, V. M. Tikhomirov, Vypuklyi analiz i ego prilozheniya, Editorial URSS, M., 2000 | MR

[4] V. B. Demidovich, G. G. Magaril-Ilyaev, V. M. Tikhomirov, “Ekstremalnye zadachi dlya lineinykh funktsionalov na chebyshevskikh prostranstvakh”, Fundament. i prikl. matem., 11:2 (2005), 87–100 | MR | Zbl

[5] R. Rokafellar, Vypuklyi analiz, Mir, M., 1973 | MR | Zbl

[6] I. Ekland, R. Temam, Vypuklyi analiz i variatsionnye problemy, Mir, M., 1979 | MR | Zbl