Nevanlinna characteristics of sequences of meromorphic functions and Julia’s exceptional functions

Author A. Ya. Khrystiyanyn, O. B. Khylynska, A. A. Kondratyuk
khrystiyanyn@ukr.net, olya_khyl@ukr.net, kond@franko.lviv.ua
Ivan Franko National University of Lviv

Abstract Uniformly convergent sequences of meromorphic functions in the Caratheodory-Landau sense on annuli are considered. We prove that the sequences of their Nevanlinna type characteristics converge uniformly on intervals. The result is applied to the study of the Nevanlinna characteristics of Julia's exceptional functions.
Keywords Nevanlinna characteristics; Julia's exceptional functions
DOI
doi:10.30970/ms.36.1.65-72
Reference 1. Ostrowski A. Uber Folgen analytischer Funktionen und einige Versch.arfungen des Picardschen satzes// Mathematische Zeitschrift. – 1925. – V.24, №1. – P. 215–258.

 2. Julia G. Le.cons sur les fonctions uniformes `a point singulier essentiel isole. – Gauthier-Villars, Paris, 1924.

 3. Carath.eodory C., Landau E. Beitr.age zur Konvergenz von Funktionenfolgen// Sitzungsber. Kon. Preuss. Akad. Wiss. Berlin. – 1911. – P. 587–613.

 4. Markushevich A.I. Theory of analytic functions. V.1. – Moscow: Nauka, 1967. (in Russian)

 5. Khrystiyanyn A.Ya., Kondratyuk A.A. On the Nevanlinna Theory for meromorphic functions on annuli. I// Mat. Stud. – 2005. – V.23, №1. – P. 19–30.

 6. Montel P. Lecons sur les familles normales de fonctions analytiques et leurs applications, Gauthier-Villars, Paris, 1927.

 7. Lehto I., Virtanen K.I. On the behaviour of meromorphic functions in the neigbourhood of an isolated singularity// Ann. Acad. Sci. Fenn. – 1957. – V.240. – P. 1–9.

 8. Goldberg A.A., Ostrovski I.V. Distibution of values of meromorphic functions. – Moscow: Nauka, 1970. (in Russian)

 9. Kondratyuk A., Laine I. Meromorphic functions in multiply connected domains// Fourier series methods in complex analysis (Mekrij.arvi, 2005), Univ. Joensuu Dept. Math. Rep. – 2006. – V.10. – P. 9–111.
Pages 65-72
Volume 36
Issue 1
Year 2011
Journal Matematychni Studii
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