Geodesic
On Extrapolation of Polynomials with Real Coefficients to the Complex Plane
Matematičeskie zametki, Tome 106 (2019) no. 4, pp. 543-548 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

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. 
@article{MZM_2019_106_4_a5,
     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},
     year = {2019},
     volume = {106},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a5/}
}
TY  - JOUR
AU  - A. S. Kochurov
AU  - V. M. Tikhomirov
TI  - On Extrapolation of Polynomials with Real Coefficients to the Complex Plane
JO  - Matematičeskie zametki
PY  - 2019
SP  - 543
EP  - 548
VL  - 106
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a5/
LA  - ru
ID  - MZM_2019_106_4_a5
ER  - 
%0 Journal Article
%A A. S. Kochurov
%A V. M. Tikhomirov
%T On Extrapolation of Polynomials with Real Coefficients to the Complex Plane
%J Matematičeskie zametki
%D 2019
%P 543-548
%V 106
%N 4
%U http://geodesic.mathdoc.fr/item/MZM_2019_106_4_a5/
%G ru
%F MZM_2019_106_4_a5
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