Generalization of the fricke theorem on entire functions of finite index
We prove that, for every sequence (a k) of complex numbers satisfying the conditions Σ(1/|a k |) < ∞ and |a k+1| − |a k | ↗ ∞ (k → ∞), there exists a continuous functionl decreasing to 0 on [0, + ∞] and such that f(z) = Π(1 −z/|a k |) is an entire function of finite l-index....
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| Date: | 1996 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
| Published: |
Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5338 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865792547949903872 |
|---|---|
| author | Sheremeta, M. M. Шеремета, М. М. |
| author_facet | Sheremeta, M. M. Шеремета, М. М. |
| author_institution_txt_mv | [
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"author": "М. М. Шеремета",
"institution": "Львiв. нац. ун-т"
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| author_sort | Sheremeta, M. M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:30:31Z |
| description | We prove that, for every sequence (a k) of complex numbers satisfying the conditions Σ(1/|a k |) < ∞ and |a k+1| − |a k | ↗ ∞ (k → ∞), there exists a continuous functionl decreasing to 0 on [0, + ∞] and such that f(z) = Π(1 −z/|a k |) is an entire function of finite l-index. |
| first_indexed | 2026-03-24T03:14:50Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5338 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:14:50Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/40/cb60b9354699e70a3e393cd3a488e540.pdf |
| spelling | umjimathkievua-article-53382020-03-18T21:30:31Z Generalization of the fricke theorem on entire functions of finite index Уточнення однієї теореми Фріке про цілі функції обмеженого індексу Sheremeta, M. M. Шеремета, М. М. We prove that, for every sequence (a k) of complex numbers satisfying the conditions Σ(1/|a k |) < ∞ and |a k+1| − |a k | ↗ ∞ (k → ∞), there exists a continuous functionl decreasing to 0 on [0, + ∞] and such that f(z) = Π(1 −z/|a k |) is an entire function of finite l-index. Доведено, що для кожної послідовності (a k) комплексних чисел, яка задовольняє умови Σ(1/|a k |) < ∞ and |a k+1| − |a k | ↗ ∞ (k → ∞), існує неперервна спадна до 0 на [0, + ∞], функція l така, що f(z) = Π(1 −z/|a k |) є цілою функцією обмеженого l-індексу. Institute of Mathematics, NAS of Ukraine 1996-03-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5338 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 3 (1996); 412-417 Український математичний журнал; Том 48 № 3 (1996); 412-417 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5338/7367 https://umj.imath.kiev.ua/index.php/umj/article/view/5338/7368 Copyright (c) 1996 Sheremeta M. M. |
| spellingShingle | Sheremeta, M. M. Шеремета, М. М. Generalization of the fricke theorem on entire functions of finite index |
| title | Generalization of the fricke theorem on entire functions of finite index |
| title_alt | Уточнення однієї теореми Фріке про цілі функції обмеженого індексу |
| title_full | Generalization of the fricke theorem on entire functions of finite index |
| title_fullStr | Generalization of the fricke theorem on entire functions of finite index |
| title_full_unstemmed | Generalization of the fricke theorem on entire functions of finite index |
| title_short | Generalization of the fricke theorem on entire functions of finite index |
| title_sort | generalization of the fricke theorem on entire functions of finite index |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5338 |
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