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Wiman’s type inequality for some double power series

Author A. O. Kuryliak, L. O. Shapovalovska, O. B. Skaskiv
kurylyak88@gmail.com, shap.ludmila@gmail.com, matstud@franko.lviv.ua
Ivan Franko National University of Lviv

Abstract In this paper we prove some analogue of Wiman's inequality for analytic functions f(z1,z2) in the domain T={zC2:|z1|<1, |z2|<+}. The obtained inequality is sharp.
Keywords maximum modulus; maximal term; double power series; Wiman’s type inequality
Reference 1. Polya G., Szego G. Aufgaben und LehrsЁatze aus der Analysis, V.2. – Berlin, Springer, 1925.

2. Goldberg A.A., Levin B.Ja., Ostrovsky I.V., Entire and meromorphic functions. – Results of scientific and technical. modern. probl. mat. fundam. guide. VINITI, 1990, V.85, P. 5–186.

3. Suleymanov N.М. Wiman-Valiron’s type inequalities for power series with bounded radii of convergence and its sharpness// DAN SSSR. – 1980. – V.253, №4. – P. 822–824. (in Russian)

4. K.ovari T. On the maximum modulus and maximal term of functions analytic in the unit disc// J. London Math. Soc. – 1966. – V.41. – P. 129–137.

5. Gopala Krishna J., Nagaraja Rao I.H. Generalised inverse and probability techniques and some fundamental growth theorems in Ck// J. Indian Math. Soc. – 1977. – V.41. – P. 203–219.

6. Fenton P. C. Wiman–Valiron theory in two variables// Trans. Amer. Math. Soc. – 1995. – V.347, №11. – P. 4403–4412.

7. Schumitzky A. Wiman-Valiron theory for functions of several complex variables. – Ph. D. Thesis: Cornel. Univ., 1965.

8. Kuryliak A.O., Skaskiv O.B. Wiman’s type inequalities without exceptional sets for random entire functions of several variables// Mat. Stud. – 2012. – V.38, №1. – P. 35–50.

9. Skaskiv O.B., Zrum O.V. Wiman’s type inequality for entire functions of two complex variables with rapidly oscilic coefficient// Mat. metods and fys.-mekh. polya. – 2005. – V.48, №4. – P. 78–87. (in Ukrainian)

10. Skaskiv O.B., Zrum O.V. On inprovement of Fenton’s inequality for entire functions of two complex variables// Math. Bull. Shevchenko Sci. Soc. – 2006. – V.3. – P. 56–68. (in Ukrainian)

11. Zrum O.V., Skaskiv O.B. On Wiman’s inequality for random entire functions of two variables// Mat. Stud. – 2005. – V.23, №2. – P. 149–160. (in Ukrainian)

Pages 134-141
Volume 39
Issue 2
Year 2013
Journal Matematychni Studii
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