Integral Estimates of Lengths of Level Lines of Rational Functions and Zolotarev's Problem
Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 331-337.

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

Integral estimates of lengths of level lines (lemniscates) of rational functions of a complex variable are obtained. These estimates are related to the problem of separation of compact sets by rational functions and to Zolotarev's problem.
Keywords: integral estimate, rational function, separation of compact sets.
@article{MZM_2013_94_3_a1,
     author = {V. I. Danchenko},
     title = {Integral {Estimates} of {Lengths} of {Level} {Lines} of {Rational} {Functions} and {Zolotarev's} {Problem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {331--337},
     publisher = {mathdoc},
     volume = {94},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a1/}
}
TY  - JOUR
AU  - V. I. Danchenko
TI  - Integral Estimates of Lengths of Level Lines of Rational Functions and Zolotarev's Problem
JO  - Matematičeskie zametki
PY  - 2013
SP  - 331
EP  - 337
VL  - 94
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a1/
LA  - ru
ID  - MZM_2013_94_3_a1
ER  - 
%0 Journal Article
%A V. I. Danchenko
%T Integral Estimates of Lengths of Level Lines of Rational Functions and Zolotarev's Problem
%J Matematičeskie zametki
%D 2013
%P 331-337
%V 94
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a1/
%G ru
%F MZM_2013_94_3_a1
V. I. Danchenko. Integral Estimates of Lengths of Level Lines of Rational Functions and Zolotarev's Problem. Matematičeskie zametki, Tome 94 (2013) no. 3, pp. 331-337. http://geodesic.mathdoc.fr/item/MZM_2013_94_3_a1/

[1] E. I. Zolotarev, Polnoe sobranie sochinenii, Vyp. 2, Izd-vo AN SSSR, L., 1932 | Zbl

[2] A. A. Gonchar, “Otsenki rosta ratsionalnykh funktsii i nekotorye ikh prilozheniya”, Matem. sb., 72(114):3 (1967), 489–503 | MR | Zbl

[3] A. A. Gonchar, “O zadachakh E. I. Zolotareva, svyazannykh s ratsionalnymi funktsiyami”, Matem. sb., 78(120):4 (1969), 640–654 | MR | Zbl

[4] Dzh. L. Uolsh, Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi oblasti, IL, M., 1961 | MR | Zbl

[5] V. I. Danchenko, “Odin kriterii suschestvovaniya otsenki proizvodnoi ratsionalnoi funktsii”, Matem. zametki, 78:4 (2005), 493–502 | DOI | MR | Zbl

[6] I. I. Privalov, Vvedenie v teoriyu funktsii kompleksnogo peremennogo, Nauka, M., 1977 | MR

[7] G. M. Goluzin, Geometricheskaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1966 | MR | Zbl