On zeros of functions of given proximate formal order analytic in a half-plane
We describe sequences of zeros of functionsf≢0 that are analytic in the half-plane ℂ+={z:Rez> and satisfy the condition $$\forall \varepsilon > 0\exists c_1 \in (0; + \infty )\forall z \in \mathbb{C}_{\text{ + }} :\left| {f(z)} \right| \leqslant c_1 \exp \left( {(\sigma + \varepsilon...
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| Date: | 1999 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Ukrainian English |
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Institute of Mathematics, NAS of Ukraine
1999
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4679 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510835144654848 |
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| author | Vynnyts’kyi, B. V. Sharan, V.L. Винницький, Б. В. Шаран, В. Л. |
| author_facet | Vynnyts’kyi, B. V. Sharan, V.L. Винницький, Б. В. Шаран, В. Л. |
| author_sort | Vynnyts’kyi, B. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:11:21Z |
| description | We describe sequences of zeros of functionsf≢0 that are analytic in the half-plane ℂ+={z:Rez> and satisfy the condition $$\forall \varepsilon > 0\exists c_1 \in (0; + \infty )\forall z \in \mathbb{C}_{\text{ + }} :\left| {f(z)} \right| \leqslant c_1 \exp \left( {(\sigma + \varepsilon )\left| z \right|\eta (\left| z \right|)} \right)$$ where 0≤σ |
| first_indexed | 2026-03-24T03:03:18Z |
| format | Article |
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| id | umjimathkievua-article-4679 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian English |
| last_indexed | 2026-03-24T03:03:18Z |
| publishDate | 1999 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/a7/d9e8862f607d7ab620e04bec4268e4a7.pdf |
| spelling | umjimathkievua-article-46792020-03-18T21:11:21Z On zeros of functions of given proximate formal order analytic in a half-plane Про нулі аналітичних у півплощині функцій заданого уточненого формального порядку Vynnyts’kyi, B. V. Sharan, V.L. Винницький, Б. В. Шаран, В. Л. We describe sequences of zeros of functionsf≢0 that are analytic in the half-plane ℂ+={z:Rez> and satisfy the condition $$\forall \varepsilon > 0\exists c_1 \in (0; + \infty )\forall z \in \mathbb{C}_{\text{ + }} :\left| {f(z)} \right| \leqslant c_1 \exp \left( {(\sigma + \varepsilon )\left| z \right|\eta (\left| z \right|)} \right)$$ where 0≤σ Наведено опис послідовностей нулів аналітичних у півплощині $ℂ_{+} = \{z : Re z > 0\}$ функцій, які задовольняють умову $$\forall \varepsilon > 0\exists c_1 \in (0; + \infty )\forall z \in \mathbb{C}_{\text{ + }} :\left| {f(z)} \right| \leqslant c_1 \exp \left( {(\sigma + \varepsilon )\left| z \right|\eta (\left| z \right|)} \right)$$ де $0 ≤ σ < +∞$ — додатна неперервно диференційовна на $[0; +∞)$ функція, для якої $xη′(x)/η(x) → 0,\; x → +∞$. Institute of Mathematics, NAS of Ukraine 1999-07-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4679 Ukrains’kyi Matematychnyi Zhurnal; Vol. 51 No. 7 (1999); 904–909 Український математичний журнал; Том 51 № 7 (1999); 904–909 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4679/6060 https://umj.imath.kiev.ua/index.php/umj/article/view/4679/6061 Copyright (c) 1999 Vynnyts’kyi B. V.; Sharan V.L. |
| spellingShingle | Vynnyts’kyi, B. V. Sharan, V.L. Винницький, Б. В. Шаран, В. Л. On zeros of functions of given proximate formal order analytic in a half-plane |
| title | On zeros of functions of given proximate formal order analytic in a half-plane |
| title_alt | Про нулі аналітичних у півплощині функцій заданого
уточненого формального порядку |
| title_full | On zeros of functions of given proximate formal order analytic in a half-plane |
| title_fullStr | On zeros of functions of given proximate formal order analytic in a half-plane |
| title_full_unstemmed | On zeros of functions of given proximate formal order analytic in a half-plane |
| title_short | On zeros of functions of given proximate formal order analytic in a half-plane |
| title_sort | on zeros of functions of given proximate formal order analytic in a half-plane |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4679 |
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