Problems in the
theory of entire functions of bounded index and functions of sine
type

M. M. Sheremeta

A connection between the functions of sine type and entire functions of bounded index is established. New problems in the theory of entire functions of bounded index and functions of sine type are formulated.

1. Левин Б. Я. О базисах показательных функций в $L^2$, Записки физ.-мат. ф-та ХГУ и Харьк. матем. об-ва., сер. 4 (1961), Вып. 27, 39--48.

2. Levin B. Ya. Lectures on entire functions, AMS, Providence, RI, 1996.

3. Левин Б. Я., Островский И. В. О малых возмущениях множества корней функций типа синуса, Изв.АН СССР, сер.мат. 43 (1979), № 1, 87–110.

4. Lepson B. Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index, Proc. Sympos. Pure Math., V.2. Amer. Math. Soc., Providence, Rhode Island, 1968, 298–307.

5. Sheremeta M. Analytic functions of bounded index, Lviv: VNTL Publishers, 1999, 141 pp.

6. Hayman W. K. Research problems in function theory, Athlow press of University of London, 1967.

7. Шеремета М. Н. О целых функциях типа синуса, Теория функций и ее прилож., Тез. докл. шк.-конф. (15-22 июня 1995г., г.Казань), Изд.Каз.фонда "Математика", 1995, С.74.

8. Fricke G. H. Functions of bounded index and their logarithmic derivative, Math. Ann. 206 (1973), 215–223.

9. Hayman W. K. Differential inequalities and local valency, Pacific J. Math. 44 (1973), 117–137.

10. Hennekemper W. Some results on functions of bounded index, Lect. Notes in Math. 747 (1979), 158–160.

11. Шеремета М. М. Уточнення однієї теореми Фріке, Укр. матем. журн. 48 (1996), № 3, 412–417.

12. Sheremeta M. M. Five open problems in theory of entire functions, Matem. studii. 6 (1996), 157–159.

	Problems in the theory of entire functions of bounded index and functions of sine type
Author	M. M. Sheremeta Faculty of Mechanics and Mathematics, Lviv National University
Abstract	A connection between the functions of sine type and entire functions of bounded index is established. New problems in the theory of entire functions of bounded index and functions of sine type are formulated.
Keywords	functions of sine type, entire functions of bounded index, theory of entire functions of bounded index, new problems in the theory
DOI	doi:10.30970/ms.15.2.217-224
Reference	1. Левин Б. Я. О базисах показательных функций в $L^2$, Записки физ.-мат. ф-та ХГУ и Харьк. матем. об-ва., сер. 4 (1961), Вып. 27, 39--48. 2. Levin B. Ya. Lectures on entire functions, AMS, Providence, RI, 1996. 3. Левин Б. Я., Островский И. В. О малых возмущениях множества корней функций типа синуса, Изв.АН СССР, сер.мат. 43 (1979), № 1, 87–110. 4. Lepson B. Differential equations of infinite order, hyperdirichlet series and entire functions of bounded index, Proc. Sympos. Pure Math., V.2. Amer. Math. Soc., Providence, Rhode Island, 1968, 298–307. 5. Sheremeta M. Analytic functions of bounded index, Lviv: VNTL Publishers, 1999, 141 pp. 6. Hayman W. K. Research problems in function theory, Athlow press of University of London, 1967. 7. Шеремета М. Н. О целых функциях типа синуса, Теория функций и ее прилож., Тез. докл. шк.-конф. (15-22 июня 1995г., г.Казань), Изд.Каз.фонда "Математика", 1995, С.74. 8. Fricke G. H. Functions of bounded index and their logarithmic derivative, Math. Ann. 206 (1973), 215–223. 9. Hayman W. K. Differential inequalities and local valency, Pacific J. Math. 44 (1973), 117–137. 10. Hennekemper W. Some results on functions of bounded index, Lect. Notes in Math. 747 (1979), 158–160. 11. Шеремета М. М. Уточнення однієї теореми Фріке, Укр. матем. журн. 48 (1996), № 3, 412–417. 12. Sheremeta M. M. Five open problems in theory of entire functions, Matem. studii. 6 (1996), 157–159.
Pages	217-224
Volume	15
Issue	2
Year	2001
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Problems in the theory of entire functions of bounded index and functions of sine type