The Bagemihl theorem for the skeleton of a~polydisk and its applications
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 35-43.

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

In this paper we prove an analog of the Bagemihl theorem for functions defined in the unit polydisk. We apply the obtained result for studying properties of functions of linearly invariant families.
Keywords: cluster set, ambiguous point, linearly invariant family.
@article{IVM_2011_6_a4,
     author = {E. G. Ganenkova},
     title = {The {Bagemihl} theorem for the skeleton of a~polydisk and its applications},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {35--43},
     publisher = {mathdoc},
     number = {6},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_6_a4/}
}
TY  - JOUR
AU  - E. G. Ganenkova
TI  - The Bagemihl theorem for the skeleton of a~polydisk and its applications
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2011
SP  - 35
EP  - 43
IS  - 6
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2011_6_a4/
LA  - ru
ID  - IVM_2011_6_a4
ER  - 
%0 Journal Article
%A E. G. Ganenkova
%T The Bagemihl theorem for the skeleton of a~polydisk and its applications
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2011
%P 35-43
%N 6
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2011_6_a4/
%G ru
%F IVM_2011_6_a4
E. G. Ganenkova. The Bagemihl theorem for the skeleton of a~polydisk and its applications. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2011), pp. 35-43. http://geodesic.mathdoc.fr/item/IVM_2011_6_a4/

[1] Bagemihl F., “Curvilinear cluster sets of arbitrary function”, Proc. Nat. Acad. Sci. USA, 41 (1955), 379–382 | DOI | MR | Zbl

[2] Young G. S., “A generalization of Bagemihl's theorem on ambiguous point”, Mich. Math. J., 5 (1958), 223–227 | DOI | MR | Zbl

[3] Bagemihl F., “Rectilinear limits of a function defined inside of sphere”, Mich. Math. J., 4 (1957), 147–150 | DOI | MR | Zbl

[4] Piranian G., “Ambiguous points of a functions continuous inside a sphere”, Mich. Math. J., 4 (1957), 151–152 | DOI | MR | Zbl

[5] Bagemihl F., “Ambiguous points of a functions harmonic inside a sphere”, Mich. Math. J., 4 (1957), 153–154 | DOI | MR | Zbl

[6] Church P. T., “Ambiguous points of a functions homeomorphic inside a sphere”, Mich. Math. J., 4 (1957), 155–156 | DOI | MR | Zbl

[7] Rippon P. J., “Ambiguous points of a functions in the unit ball of euclidean space”, Bull. Lond. Math. Soc., 15 (1983), 336–338 | DOI | MR | Zbl

[8] Pommerenke Ch., “Linear-invariante Familien analytischer Funktionen, I”, Math. Ann., 155 (1964), 108–154 | DOI | MR | Zbl

[9] Godula J., Starkov V. V., “Linearly invariant families of holomorphic functions in the unit polydisk”, Generalizations of complex analysis and their applications in physics, Banach Center Publ., 37, 1996, 115–127 | MR | Zbl

[10] Krzy.{z} J., “On the maximum modulus of univalent functions”, Bull. Pol. Acad. Sci. Math. Cl. III, 3 (1955), 203–206 | MR | Zbl

[11] Kheiman V. K., Mnogolistnye funktsii, In. lit., M., 1960, 180 pp. | MR

[12] Bieberbach L., Einführung in die konforme Abbildung, Sammlung Göschen, Berlin, 1967 | MR

[13] Campbell D. M., “Locally univalent functions with locally univalent derivatives”, Trans. Amer. Math. Soc., 162 (1971), 395–409 | DOI | MR

[14] Starkov V. V., “Teorema regulyarnosti dlya universalnykh lineino-invariantnykh semeistv funktsii”, Serdika, 11 (1985), 299–318 | MR | Zbl

[15] Godulya Ya., Starkov V. V., “Teorema regulyarnosti dlya lineino-invariantnykh semeistv funktsii v polikruge”, Izv. vuzov. Matematika, 1995, no. 8, 21–33 | MR | Zbl

[16] Godula J., Starkov V. V., “On regularity theorems for linearly invariant families of analytic functions in the unit polydisk”, Comput. Methods and Function Theory, 1997, 241–257 | MR | Zbl

[17] Godula J., Starkov V. V., “On regularity theorems for linearly invariant families of analytic functions in the unit polydisk, II”, Ann. Univ. Mariae Curie-Skłodowska Sect. A, 52:2 (1998), 15–24 | MR | Zbl

[18] Ganenkova E. G., “Teorema regulyarnosti ubyvaniya dlya analiticheskikh v polikruge funktsii”, Tr. Petrozavodsk. gos. un-ta. Ser. matem., 14, 2007, 14–30 | MR | Zbl

[19] Ganenkova E.G., “Teorema regulyarnosti ubyvaniya v lineino-invariantnykh semeistvakh funktsii”, Izv. vuzov. Matematika, 2007, no. 2, 75–78 | MR | Zbl

[20] Ganenkova E. G., “Nekotorye granichnye svoistva analiticheskikh v polikruge funktsii, obrazuyuschikh lineino-invariantnye semeistva”, Tr. Petrozavodsk. gos. un-ta. Ser. matem., 16, 2009, 12–32 | MR