On the growth of functions represented by Dirichlet series with complex coefficients on the real axis
We establish conditions under which, for a Dirichlet series $F(z) = \sum_{n = 1}^{∞} d n \exp(λ_n z)$, the inequality $⋎F(x)⋎ ≤ y(x),\quad x ≥ x_0$, implies the relation $\sum_{n = 1}^{∞} |d_n \exp(λ_n z)| ⪯ γ((1 + o(1))x)$ as $x → +∞$, where $γ$ is a nondecreasing function on $(−∞,+∞)$....
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| Date: | 1997 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1997
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5165 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511367802388480 |
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| author | Vynnyts’kyi, B. V. Винницький, Б. В. |
| author_facet | Vynnyts’kyi, B. V. Винницький, Б. В. |
| author_sort | Vynnyts’kyi, B. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:26:15Z |
| description | We establish conditions under which, for a Dirichlet series $F(z) = \sum_{n = 1}^{∞} d n \exp(λ_n z)$, the inequality $⋎F(x)⋎ ≤ y(x),\quad x ≥ x_0$, implies the relation $\sum_{n = 1}^{∞} |d_n \exp(λ_n z)| ⪯ γ((1 + o(1))x)$ as $x → +∞$, where $γ$ is a nondecreasing function on $(−∞,+∞)$. |
| first_indexed | 2026-03-24T03:11:46Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5165 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:11:46Z |
| publishDate | 1997 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/3c/16003935fd445a6e6e55fa0b33384f3c.pdf |
| spelling | umjimathkievua-article-51652020-03-18T21:26:15Z On the growth of functions represented by Dirichlet series with complex coefficients on the real axis Про зростання функцій, зображених рядами Діріхле з комплексними показниками, на дійсній осі Vynnyts’kyi, B. V. Винницький, Б. В. We establish conditions under which, for a Dirichlet series $F(z) = \sum_{n = 1}^{∞} d n \exp(λ_n z)$, the inequality $⋎F(x)⋎ ≤ y(x),\quad x ≥ x_0$, implies the relation $\sum_{n = 1}^{∞} |d_n \exp(λ_n z)| ⪯ γ((1 + o(1))x)$ as $x → +∞$, where $γ$ is a nondecreasing function on $(−∞,+∞)$. Знайдено умови, за яких для ряду Діріхле $F(z) = \sum_{n = 1}^{∞} d n \exp(λ_n z)$ із нерівності $⋎F(x)⋎ ≤ y(x),\quad x ≥ x_0$, випливає, що$\sum_{n = 1}^{∞} |d_n \exp(λ_n z)| ⪯ γ((1 + o(1))x)$, $x → +∞$ де $γ$— неспадпа функція на $(−∞,+∞)$. Institute of Mathematics, NAS of Ukraine 1997-12-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5165 Ukrains’kyi Matematychnyi Zhurnal; Vol. 49 No. 12 (1997); 1610–1616. December Український математичний журнал; Том 49 № 12 (1997); 1610–1616. December 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/5165/7026 https://umj.imath.kiev.ua/index.php/umj/article/view/5165/7027 Copyright (c) 1997 Vynnyts’kyi B. V. |
| spellingShingle | Vynnyts’kyi, B. V. Винницький, Б. В. On the growth of functions represented by Dirichlet series with complex coefficients on the real axis |
| title | On the growth of functions represented by Dirichlet series with complex coefficients on the real axis |
| title_alt | Про зростання функцій, зображених рядами
Діріхле з комплексними показниками, на дійсній осі |
| title_full | On the growth of functions represented by Dirichlet series with complex coefficients on the real axis |
| title_fullStr | On the growth of functions represented by Dirichlet series with complex coefficients on the real axis |
| title_full_unstemmed | On the growth of functions represented by Dirichlet series with complex coefficients on the real axis |
| title_short | On the growth of functions represented by Dirichlet series with complex coefficients on the real axis |
| title_sort | on the growth of functions represented by dirichlet series with complex coefficients on the real axis |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5165 |
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