Geodesic
On a Variational Method for Univalent Functions
Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 240-250.

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

In the paper, the construction of a variational method for univalent functions is suggested; this construction uses the factorization theorem. As a consequence, an analog of the Goluzin variational formula is obtained.
Keywords: variational method, univalent function, factorization theorem, conformal mapping, Goluzin variational method
Mots-clés : Laurent series. 
@article{MZM_2007_81_2_a7,
     author = {V. V. Kozhevnikov},
     title = {On a {Variational} {Method} for {Univalent} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {240--250},
     publisher = {mathdoc},
     volume = {81},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a7/}
}
TY  - JOUR
AU  - V. V. Kozhevnikov
TI  - On a Variational Method for Univalent Functions
JO  - Matematičeskie zametki
PY  - 2007
SP  - 240
EP  - 250
VL  - 81
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a7/
LA  - ru
ID  - MZM_2007_81_2_a7
ER  - 
%0 Journal Article
%A V. V. Kozhevnikov
%T On a Variational Method for Univalent Functions
%J Matematičeskie zametki
%D 2007
%P 240-250
%V 81
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a7/
%G ru
%F MZM_2007_81_2_a7
V. V. Kozhevnikov. On a Variational Method for Univalent Functions. Matematičeskie zametki, Tome 81 (2007) no. 2, pp. 240-250. http://geodesic.mathdoc.fr/item/MZM_2007_81_2_a7/

[1] V. D. Erokhin, “O konformnykh preobrazovaniyakh kolets i ob osnovnom bazise prostranstva funktsii, analiticheskikh v elementarnoi okrestnosti kontinuuma”, Dokl. AN SSSR, 120:4 (1958), 689–692 | MR | Zbl

[2] S. A. Gelfer, “O rasprostranenii variatsionnogo metoda Goluzina–Shiffera na mnogosvyaznye oblasti”, Dokl. AN SSSR, 142:3 (1962), 503–506 | MR | Zbl

[3] G. M. Goluzin, “Metod variatsii v konformnom otobrazhenii. I”, Matem. sb., 19 (1946), 203–236 | MR | Zbl

[4] V. V. Kozhevnikov, “Faktorizatsiya konformnykh otobrazhenii i variatsii odnolistnykh funktsii”, Dokl. RAN, 375:3 (2000), 305–306 | MR | Zbl

[5] V. V. Kozhevnikov, “Kusochno odnolistnye variatsii vtorogo poryadka”, Geometricheskii analiz i ego prilozheniya, Tezisy dokladov Volgogradskoi konferentsii, Izd-vo Volgogradskogo un-ta, Volgograd, 2004, 80–82

[6] V. V. Kozhevnikov, “Ob odnoi forme pryamogo variatsionnogo metoda dlya odnolistnykh funktsii”, Izv. vuzov. Ser. matem., 2004, no. 4, 28–37 | MR | Zbl

[7] K. I. Babenko, K teorii ekstremalnykh zadach dlya odnolistnykh funktsii klassa $S$, Tr. MIAN, 101, Nauka, M., 1972 | MR | Zbl