Lemniscate zone and distortion theorems for multivalent functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 33, Tome 458 (2017), pp. 17-30 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The impact of the connectivity of some lemniscates of the multivalent function on the absolute value of this function or its derivative is considered.
@article{ZNSL_2017_458_a2,
     author = {V. N. Dubinin},
     title = {Lemniscate zone and distortion theorems for multivalent functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {17--30},
     year = {2017},
     volume = {458},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a2/}
}
TY  - JOUR
AU  - V. N. Dubinin
TI  - Lemniscate zone and distortion theorems for multivalent functions
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2017
SP  - 17
EP  - 30
VL  - 458
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a2/
LA  - ru
ID  - ZNSL_2017_458_a2
ER  - 
%0 Journal Article
%A V. N. Dubinin
%T Lemniscate zone and distortion theorems for multivalent functions
%J Zapiski Nauchnykh Seminarov POMI
%D 2017
%P 17-30
%V 458
%U http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a2/
%G ru
%F ZNSL_2017_458_a2
V. N. Dubinin. Lemniscate zone and distortion theorems for multivalent functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 33, Tome 458 (2017), pp. 17-30. http://geodesic.mathdoc.fr/item/ZNSL_2017_458_a2/

[1] W. K. Hayman, Research Problems in Function Theory., The Athlone Press University of London, London, 1967 | MR | Zbl

[2] P. Erdos, Some of My Favorite Unsolved Problems., A Tribute to Paul Erdős, Cambridge Univ. Press, Cambridge, 1990 | MR

[3] A. Eremenko, L. Lempert, “An extremal problem for polynomials”, Proc. Amer. Math. Soc., 122:1 (1994), 191–193 | DOI | MR | Zbl

[4] A. Eremenko, “A Markov-type inequality for arbitrary plane continua”, Proc. Amer. Math. Soc., 135:5 (2007), 1505–1510 | DOI | MR | Zbl

[5] V. N. Dubinin, “Neravenstvo markovskogo tipa i nizhnyaya otsenka modulei kriticheskikh znachenii polinomov”, Dokl. RAN, 451:5 (2013), 495–497 | DOI | Zbl

[6] V. Dubinin, “Four-point distortion theorem for complex polynomials”, Complex Variables and Elliptic Equations, 59:1 (2014), 59–66 | DOI | MR | Zbl

[7] V. N. Dubinin, “Ob odnoi ekstremalnoi zadache dlya kompleksnykh polinomov s ogranicheniyami na ikh kriticheskie znacheniya”, Sib. mat. zh., 55:1 (2014), 79–89 | MR | Zbl

[8] V. N. Dubinin, “Kriticheskie znacheniya i moduli proizvodnoi v nulyakh kompleksnogo polinoma”, Zap. nauchn. semin. POMI, 449, 2016, 60–68 | MR

[9] V. N. Dubinin, “Ekstremalnaya zadacha dlya proizvodnoi ratsionalnoi funktsii”, Mat. zametki, 100:5 (2016), 732–738 | DOI | MR | Zbl

[10] V. N. Dubinin, “O logarifmicheskoi energii nulei i polyusov ratsionalnoi funktsii”, Sib. mat. zh., 57:6 (2016), 1255–1261 | DOI | MR | Zbl

[11] V. N. Dubinin, “Novaya versiya krugovoi simmetrizatsii s prilozheniyami k $p$-listnym funktsiyam”, Mat. sb., 203:7 (2012), 79–94 | DOI | MR | Zbl

[12] V. N. Dubinin, “Krugovaya simmetrizatsiya kondensatorov na rimanovykh poverkhnostyakh”, Mat. sb., 206:1 (2015), 69–96 | DOI | MR | Zbl

[13] V. N. Dubinin, A. S. Afanaseva-Grigoreva, “O lemniskatakh ratsionalnykh funktsii”, Dalnevostochnyi mat. zh., 17:2 (2017), 201–209

[14] V. N. Dubinin, “Simmetrizatsiya kondensatorov i neravenstva dlya mnogolistnykh v kruge funktsii”, Mat. zametki, 94:6 (2013), 846–856 | DOI | MR | Zbl

[15] V. N. Dubinin, “Teoremy iskazheniya dlya funktsii, $p$-listnykh v srednem po okruzhnosti”, Zap. nauchn. semin. POMI, 440, 2015, 43–56 | MR

[16] V. N. Dubinin, “Neravenstva dlya modulei funktsii, $p$-listnykh v srednem po okruzhnosti”, Zap. nauchn. semin. POMI, 429, 2014, 44–54

[17] N. I. Akhiezer, Elementy teorii ellipticheskikh funktsii, Nauka, M., 1970 | MR

[18] A. B. Bogatyrev, “Chebyshëvskoe predstavlenie ratsionalnykh funktsii”, Mat. sb., 201:11 (2010), 19–40 | DOI | MR | Zbl

[19] A. B. Bogatyrev, How Many Zolotarev Fractions are There?, 2015, arXiv: 1511.05346 | MR

[20] M. M. Gkhashim, V. N. Malozemov, G. Sh. Tamasyan, Drobi Zolotareva, Seminar po konstruktivnomu negladkomu analizu i nedifferentsiruemoi optimizatsii “CNSA NDO”, , 2016 http://www.apmath.spbu.ru/cnsa/

[21] A. Gurvits, R. Kurant, Teoriya funktsii, M., 1968 | MR