On the boundedness of $l$-index of a canonical product of zero genus and of a Blaschke product (in Ukrainian)

Yu.S.Trukhan; M.M.Sheremeta

Conditions on zeros under which a canonical product of zero genus is entire function of bounded $l$-index and a Blaschke product is an analytic function of bounded $l$-index in the unit disk are investigated.

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. --- AMS, Providence, Phode Island, 1968. --- P.298--307.

3. Fricke G. Entire functions having positive zeros// Indian J. Pure Appl. Math. --- 1996. --- V.5,№5. --- P.412--417.

4. Шеремета М.М. Уточнення однієї теореми Фріке// Укр. мат. журн. --- 1996. --- T.48, № 9. --- C.1166--1182.

5. Chyzhykov I.E., Sheremeta M.M. Boundedness of $l$-index for entire functions of zero genus// Matematychni Studii. --- 2001. --- V.16, № 2. --- P.124--130.

6. Чижиков І.Е., Шеремета М.М. Про обмеженість $l$-індексу цілих функцій нульового роду// Доп. НАН України. --- 2003. --- № 7. --- C.33--39.

7. Gol'dberg A.A., Sheremeta M.M. On the boundedness of $l$-index of canonical products// Ukr. Math. Bull. --- 2005. --- V.2, №1. --- P.53--65.

8. Trukhan Yu.S. Sheremeta M.M. On $l$-index boundedness of the Blaschke product// Matematychni Studii. --- 2003. --- V.19,№ 1. --- P.106--112.

9. Трухан Ю.С. До обмеженості $l$-індексу добутку Бляшке// Вісник Львів. ун-ту, cерія мех.-мат. --- 2004. Вип. 63. --- С.143--147.

10. Трухан Ю.С. Шеремета М.М. Обмеженість $l$-індексу добутку Нафталевича-Цудзі// Укр. мат. журн. --- 2004. --- T. 56, № 2. --- C.247--256.

	On the boundedness of $l$-index of a canonical product of zero genus and of a Blaschke product (in Ukrainian)
Author	Yu.S.Trukhan, M.M.Sheremeta yurik93@mail.ru Ivan Franko National University of Lviv, Department of Function Theory and Probability Theory
Abstract	Conditions on zeros under which a canonical product of zero genus is entire function of bounded $l$-index and a Blaschke product is an analytic function of bounded $l$-index in the unit disk are investigated.
Keywords	l-index, canonical product, zero genus, Blaschke product
DOI	doi:10.30970/ms.29.1.45-51
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. --- AMS, Providence, Phode Island, 1968. --- P.298--307. 3. Fricke G. Entire functions having positive zeros// Indian J. Pure Appl. Math. --- 1996. --- V.5,№5. --- P.412--417. 4. Шеремета М.М. Уточнення однієї теореми Фріке// Укр. мат. журн. --- 1996. --- T.48, № 9. --- C.1166--1182. 5. Chyzhykov I.E., Sheremeta M.M. Boundedness of $l$-index for entire functions of zero genus// Matematychni Studii. --- 2001. --- V.16, № 2. --- P.124--130. 6. Чижиков І.Е., Шеремета М.М. Про обмеженість $l$-індексу цілих функцій нульового роду// Доп. НАН України. --- 2003. --- № 7. --- C.33--39. 7. Gol'dberg A.A., Sheremeta M.M. On the boundedness of $l$-index of canonical products// Ukr. Math. Bull. --- 2005. --- V.2, №1. --- P.53--65. 8. Trukhan Yu.S. Sheremeta M.M. On $l$-index boundedness of the Blaschke product// Matematychni Studii. --- 2003. --- V.19,№ 1. --- P.106--112. 9. Трухан Ю.С. До обмеженості $l$-індексу добутку Бляшке// Вісник Львів. ун-ту, cерія мех.-мат. --- 2004. Вип. 63. --- С.143--147. 10. Трухан Ю.С. Шеремета М.М. Обмеженість $l$-індексу добутку Нафталевича-Цудзі// Укр. мат. журн. --- 2004. --- T. 56, № 2. --- C.247--256.
Pages	45-51
Volume	29
Issue	1
Year	2008
Journal	Matematychni Studii
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