Generalizations of Nevanlinna's theorems

B.N.Khabibullin

We give a short survey on generalizations of Nevanlinna theorems on zero distribution of bounded holomorphic functions and representation of meromorphic functions in multiply connected domains. It is a part of our report on the conference on complex analysis dedicated to the memory of Anatolii Asirovich Goldberg in Lviv, May 31-June 5, 2010.

1. Kondratyuk A., Laine I. Meromorphic functions in multiply connected domains. -- Joensuu -- L'viv, 2006. -- P.~9--111.

2. Khabibullin B.N. Zero sequences of holomorphic functions, the representation of meromorphic functions and harmonic minorants// Matematicheski i Sbornik -- 2007. -- V.198, №2. -- P. 121--160 (in Russian); Eng. transl. in ``Sbornik: Mathematics''. -- 2007. -- V.198, №2. -- P. 261--298.

3. Khabibullin B.N. Dual representation of superlinear functionals and its applications in function theory. II// Izvestiya RAN -- 2001. -- V.65, №5. -- P. 167--190; Eng. trans. in ''Izvestiya: Mathematics'' -- 2001. -- V.65, №5. -- P. 1017--1039.

4. Kudasheva E.G., Khabibullin B.N. it The distribution of the zeros of holomorphic functions of moderate growth in the unit disc and the representation of meromorphic functions// Matematicheskii Sbornik -- 2009. -- V.200, №9. -- P. 95--126 (in Russian); Eng. transl. in ''Sbornik: Mathematics'' -- 2009. -- V.198, №2. -- P. 1353--1382.

	Generalizations of Nevanlinna's theorems
Author	B.N.Khabibullin khabib-bulat@mail.ru Bashkir State University, Russia, Ufa
Abstract	We give a short survey on generalizations of Nevanlinna theorems on zero distribution of bounded holomorphic functions and representation of meromorphic functions in multiply connected domains. It is a part of our report on the conference on complex analysis dedicated to the memory of Anatolii Asirovich Goldberg in Lviv, May 31-June 5, 2010.
Keywords	Nevanlinna thorem, bounded meromorphic function, multiply connected domain, zero distribution
DOI	doi:10.30970/ms.34.2.197-206
Reference	1. Kondratyuk A., Laine I. Meromorphic functions in multiply connected domains. -- Joensuu -- L'viv, 2006. -- P.~9--111. 2. Khabibullin B.N. Zero sequences of holomorphic functions, the representation of meromorphic functions and harmonic minorants// Matematicheski i Sbornik -- 2007. -- V.198, №2. -- P. 121--160 (in Russian); Eng. transl. in ``Sbornik: Mathematics''. -- 2007. -- V.198, №2. -- P. 261--298. 3. Khabibullin B.N. Dual representation of superlinear functionals and its applications in function theory. II// Izvestiya RAN -- 2001. -- V.65, №5. -- P. 167--190; Eng. trans. in ''Izvestiya: Mathematics'' -- 2001. -- V.65, №5. -- P. 1017--1039. 4. Kudasheva E.G., Khabibullin B.N. it The distribution of the zeros of holomorphic functions of moderate growth in the unit disc and the representation of meromorphic functions// Matematicheskii Sbornik -- 2009. -- V.200, №9. -- P. 95--126 (in Russian); Eng. transl. in ''Sbornik: Mathematics'' -- 2009. -- V.198, №2. -- P. 1353--1382.
Pages	197-206
Volume	34
Issue	2
Year	2010
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html