On behaviour of integral functions represented by the Dirichlet series on the real axis
Conditions are found under which for an entire function $f$ represented by a Dirichlet series with finite Ritt order on some sequence $(x_k), 0<x_k↑\infty$, as $k→\infty$ one has $| f (x_k) | = M_f((1+o(1)x_k),M_f(x)=sup\{|f(z)|:{\rm Re} \ z\leq x\}$.
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Russisch |
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Institute of Mathematics, NAS of Ukraine
2025
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/9367 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860513520070688768 |
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| author | Vinnitsky , В. V. Sorokivsky , V. M. Винницкий , Б. В. Сорокивский , В. М. |
| author_facet | Vinnitsky , В. V. Sorokivsky , V. M. Винницкий , Б. В. Сорокивский , В. М. |
| author_sort | Vinnitsky , В. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2025-06-30T14:20:55Z |
| description | Conditions are found under which for an entire function $f$ represented by a Dirichlet series with finite Ritt order on some sequence $(x_k), 0<x_k↑\infty$, as $k→\infty$ one has $| f (x_k) | = M_f((1+o(1)x_k),M_f(x)=sup\{|f(z)|:{\rm Re} \ z\leq x\}$. |
| first_indexed | 2026-03-24T03:45:59Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-9367 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus |
| last_indexed | 2026-03-24T03:45:59Z |
| publishDate | 2025 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/df/8361f81c724d20f2c6319adb21c276df.pdf |
| spelling | umjimathkievua-article-93672025-06-30T14:20:55Z On behaviour of integral functions represented by the Dirichlet series on the real axis О поведении на действительной оси целых функций, представленных рядами Дирихле Vinnitsky , В. V. Sorokivsky , V. M. Винницкий , Б. В. Сорокивский , В. М. - Conditions are found under which for an entire function $f$ represented by a Dirichlet series with finite Ritt order on some sequence $(x_k), 0<x_k↑\infty$, as $k→\infty$ one has $| f (x_k) | = M_f((1+o(1)x_k),M_f(x)=sup\{|f(z)|:{\rm Re} \ z\leq x\}$. Найдены условия, при которых для целой функции $f$ представленной рядом Дирихле, с конечным порядком по Ритту на некоторой последовательности $(x_k), 0<x_k↑\infty$, при $k→\infty$ выполняется $| f (x_k) | = M_f((1+o(1)x_k),M_f(x)=sup\{|f(z)|:{\rm Re} \ z\leq x\}$. Знайдені умови, зa яких для функції $f$, заданої рядом Діріхле, з скінченним порядком Рітом на деякій послідовності $(x_k), 0<x_k↑\infty$, при $k→\infty$ виконується $| f (x_k) | = M_f((1+o(1)x_k),M_f(x)=sup\{|f(z)|:{\rm Re} \ z\leq x\}$. Institute of Mathematics, NAS of Ukraine 2025-06-30 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/9367 Ukrains’kyi Matematychnyi Zhurnal; Vol. 43 No. 2 (1991); 265-269 Український математичний журнал; Том 43 № 2 (1991); 265-269 1027-3190 rus https://umj.imath.kiev.ua/index.php/umj/article/view/9367/10517 Copyright (c) 1991 Б. В. Винницкий , В. М. Сорокивский |
| spellingShingle | Vinnitsky , В. V. Sorokivsky , V. M. Винницкий , Б. В. Сорокивский , В. М. On behaviour of integral functions represented by the Dirichlet series on the real axis |
| title | On behaviour of integral functions represented by the Dirichlet series on the real axis |
| title_alt | О поведении на действительной оси целых функций, представленных рядами Дирихле |
| title_full | On behaviour of integral functions represented by the Dirichlet series on the real axis |
| title_fullStr | On behaviour of integral functions represented by the Dirichlet series on the real axis |
| title_full_unstemmed | On behaviour of integral functions represented by the Dirichlet series on the real axis |
| title_short | On behaviour of integral functions represented by the Dirichlet series on the real axis |
| title_sort | on behaviour of integral functions represented by the dirichlet series on the real axis |
| topic_facet | - |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/9367 |
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