Geodesic
On the polynomials, the least deviating from zero in $L[-1,1]$ metrics (Second part)
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 2, pp. 123-136 
V. È. Gheit. On the polynomials, the least deviating from zero in $L[-1,1]$ metrics (Second part). Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 4 (2001) no. 2, pp. 123-136. http://geodesic.mathdoc.fr/item/SJVM_2001_4_2_a1/
@article{SJVM_2001_4_2_a1,
     author = {V. \`E. Gheit},
     title = {On the polynomials, the least deviating from zero in $L[-1,1]$ metrics {(Second} part)},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {123--136},
     year = {2001},
     volume = {4},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2001_4_2_a1/}
}
TY  - JOUR
AU  - V. È. Gheit
TI  - On the polynomials, the least deviating from zero in $L[-1,1]$ metrics (Second part)
JO  - Sibirskij žurnal vyčislitelʹnoj matematiki
PY  - 2001
SP  - 123
EP  - 136
VL  - 4
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/SJVM_2001_4_2_a1/
LA  - ru
ID  - SJVM_2001_4_2_a1
ER  - 
%0 Journal Article
%A V. È. Gheit
%T On the polynomials, the least deviating from zero in $L[-1,1]$ metrics (Second part)
%J Sibirskij žurnal vyčislitelʹnoj matematiki
%D 2001
%P 123-136
%V 4
%N 2
%U http://geodesic.mathdoc.fr/item/SJVM_2001_4_2_a1/
%G ru
%F SJVM_2001_4_2_a1

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

The properties of maximum polynomials, the least deviating from zero in integral metric whose forms are calculated in the first part [5] are studied. Theorem 2.2 contains the classification of polynomials, the least deviating from zero in $L[-1,1]$ metrics with given four leading coefficients.

[1] Korkin A. N., Zolotarev G. I., “Sur une certain minimum”, Nouv. Ann. de math. Ser. 2, 12 (1873), 337–355

[2] Tikhomirov V. M., Nekotorye voprosy teorii priblizhenii, Izd-vo MGU, M., 1976 | MR

[3] Galeev E. M., “Zadacha Zolotareva v metrike $L[-1,1]$”, Mat. zametki, 17:1 (1975), 13–20 | MR | Zbl

[4] Pukhov S. V., “Ekstremalnaya zadacha o polinomakh, naimenee uklonyayuschikhsya ot nulya v prostranstve $L([-1,1])$, tri starshikh koeffitsienta kotorykh zadany”, Algebraicheskie sistemy, Ivanovskii gosudarstvennyi universitet, Ivanovo, 1991, 142–149 | MR

[5] Geit V. E., “O polinomakh, naimenee uklonyayuschikhsya ot nulya v metrike $L[-1,1]$”, Sib. zhurn. vychisl. matematiki / RAN. Sib. otd-nie. — Novosibirsk, 2:3 (1999), 223–238

[6] Geit V. E., O forme zolotarevskikh polinomov v prostranstve $L[-1,1]$, 22.04.98, No 1228-V98, VINITI, M., 1998

[7] Geit V. E., Reshenie $L$-problemy Zolotareva v odnom chastnom sluchae, 27.11.98, No 3492-V98, VINITI, M., 1998