Preservation of
$l$-index boundedness under zeros shifts

М. Т.  Bordulyak; і. Е.  Chyzhykov; М. М.  Sheremeta

For entire functions represented by canonical products with zeros on a finite system of curves of regular rotation conditions on shifts of zeros preserving boundedness of $l$-index are found.

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

2. 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.

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

4. Бордуляк M.\ T., Шеремета M.\ Н. О существовании целых функций ограниченного $l$-индекса и $l$-регулярного роста, Укр. мат. журн. 48 (1996), № 9, 1166--1182

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

6. Sheremeta M. M. Problems in the theory of entire functions of bounded index and functions of sine type, Matem. Studii. 15 (2001), № 2, 217–224.

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

8. Балашов С. К. О целых функциях конечного порядка с корнями на кривых правильного вращения, Изв. АН СССР. Сер. мат. 37 (1973), 603–629.

9. Левин Б. Я. Распределение корней целых функций, М.: Гостехиздат, 1956, 632 с.

10. Chyzhykov I.E., Sheremeta M.M. Boundedness of $l$-index for entire functions of zero genus, Mat. Studii 16 (2001), № 2, 124--130.

	Preservation of $l$-index boundedness under zeros shifts
Author	М. Т. Bordulyak, і. Е. Chyzhykov, М. М. Sheremeta Faculty of Mechanics and Mathematics, Lviv Ivan Franko National,University
Abstract	For entire functions represented by canonical products with zeros on a finite system of curves of regular rotation conditions on shifts of zeros preserving boundedness of $l$-index are found.
Keywords	entire functions, canonical products, zeros on a finite system of curves of regular rotation, conditions on shifts of zeros,
DOI	doi:10.30970/ms.19.1.21-30
Reference	1. Sheremeta M. M. Analytic functions of bounded index, Lviv: VNTL Publishers, 1999, 141 pp. 2. 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. 3. Fricke G. H. Functions of bounded index and their logarithmic derivative, Math. Ann. 206 (1973), 215–223. 4. Бордуляк M.\ T., Шеремета M.\ Н. О существовании целых функций ограниченного $l$-индекса и $l$-регулярного роста, Укр. мат. журн. 48 (1996), № 9, 1166--1182 5. Hayman W. K. Differential inequalities and local valency, Pacific J. Math. 44 (1973), 117–137. 6. Sheremeta M. M. Problems in the theory of entire functions of bounded index and functions of sine type, Matem. Studii. 15 (2001), № 2, 217–224. 7. Sheremeta M. M. Five open problems in theory of entire functions, Matem. studii. 6 (1996), 157–159. 8. Балашов С. К. О целых функциях конечного порядка с корнями на кривых правильного вращения, Изв. АН СССР. Сер. мат. 37 (1973), 603–629. 9. Левин Б. Я. Распределение корней целых функций, М.: Гостехиздат, 1956, 632 с. 10. Chyzhykov I.E., Sheremeta M.M. Boundedness of $l$-index for entire functions of zero genus, Mat. Studii 16 (2001), № 2, 124--130.
Pages	21-30
Volume	19
Issue	1
Year	2003
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

Preservation of $l$-index boundedness under zeros shifts