On zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane
We obtain the description of the zeros, singular boundary functions, and modules of angular boundary values of the functions $f \neq 0$ which are analytic in the half-plane $C_{+} = \{ z : \Re z > 0 \}$ and satisfy the condition $$( \forall \varepsilon > 0 ) ( \exists c_1 > 0 )...
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| Datum: | 2004 |
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| Hauptverfasser: | , , , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
2004
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/3803 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860509934958936064 |
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| author | Vynnyts’kyi, B. V. Sharan, V.L. Винницкий, Б. В. Шаран, В. Л. Винницкий, Б. В. Шаран, В. Л. |
| author_facet | Vynnyts’kyi, B. V. Sharan, V.L. Винницкий, Б. В. Шаран, В. Л. Винницкий, Б. В. Шаран, В. Л. |
| author_sort | Vynnyts’kyi, B. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:09:24Z |
| description | We obtain the description of the zeros, singular boundary functions, and modules of angular boundary
values of the functions $f \neq 0$ which are analytic in the half-plane $C_{+} = \{ z : \Re z > 0 \}$ and satisfy the
condition
$$( \forall \varepsilon > 0 ) ( \exists c_1 > 0 ) (\forall z \in \mathbb{Ñ}_{+} ): | f ( z ) | \leq c_1 \exp ( (\sigma + \varepsilon) | z \eta ( | z | ) ), $$,
where $0 \leq \sigma < +\infty$ is a given number and $\eta$ is a positive function continuously differentiable on
$[0; +\infty$ and such that $t\eta'(t)/\eta(t) \rightarrow 0$ as $t \rightarrow + \infty$/
|
| first_indexed | 2026-03-24T02:49:00Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-3803 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:49:00Z |
| publishDate | 2004 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/4e/8b620edcb978cd0c7a9daa678414834e.pdf |
| spelling | umjimathkievua-article-38032020-03-18T20:09:24Z On zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane О нулях, сингулярных граничных функциях и модулях угловых предельных значений одного класса функций, аналитических в полуплоскости Vynnyts’kyi, B. V. Sharan, V.L. Винницкий, Б. В. Шаран, В. Л. Винницкий, Б. В. Шаран, В. Л. We obtain the description of the zeros, singular boundary functions, and modules of angular boundary values of the functions $f \neq 0$ which are analytic in the half-plane $C_{+} = \{ z : \Re z > 0 \}$ and satisfy the condition $$( \forall \varepsilon > 0 ) ( \exists c_1 > 0 ) (\forall z \in \mathbb{Ñ}_{+} ): | f ( z ) | \leq c_1 \exp ( (\sigma + \varepsilon) | z \eta ( | z | ) ), $$, where $0 \leq \sigma < +\infty$ is a given number and $\eta$ is a positive function continuously differentiable on $[0; +\infty$ and such that $t\eta'(t)/\eta(t) \rightarrow 0$ as $t \rightarrow + \infty$/ Отримано опис послідовностей нулів, сингулярних граничних функцій і модулів кутових граничних значень аналітичних у півплощині $C_{+} = \{ z : \Re z > 0 \}$ функцій $f \neq 0$, які задовольня- ють умову $$( \forall \varepsilon > 0 ) ( \exists c_1 > 0 ) (\forall z \in \mathbb{Ñ}_{+} ): | f ( z ) | \leq c_1 \exp ( (\sigma + \varepsilon) | z \eta ( | z | ) ), $$ де $0 \leq \sigma < +\infty$ — задане число, $\eta$ —додатна неперервно диферепційовна на $[0; +\infty$ функція, для якої $t\eta'(t)/\eta(t) \rightarrow 0$ при $t \rightarrow + \infty$. Institute of Mathematics, NAS of Ukraine 2004-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/3803 Ukrains’kyi Matematychnyi Zhurnal; Vol. 56 No. 6 (2004); 851–856 Український математичний журнал; Том 56 № 6 (2004); 851–856 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/3803/4326 https://umj.imath.kiev.ua/index.php/umj/article/view/3803/4327 Copyright (c) 2004 Vynnyts’kyi B. V.; Sharan V.L. |
| spellingShingle | Vynnyts’kyi, B. V. Sharan, V.L. Винницкий, Б. В. Шаран, В. Л. Винницкий, Б. В. Шаран, В. Л. On zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane |
| title | On zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane |
| title_alt | О нулях, сингулярных граничных функциях и модулях
угловых предельных значений одного класса функций, аналитических в полуплоскости |
| title_full | On zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane |
| title_fullStr | On zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane |
| title_full_unstemmed | On zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane |
| title_short | On zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane |
| title_sort | on zeros, singular boundary functions, and modules of angular boundary values for one class of functions analytic in a half-plane |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/3803 |
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