Lower types of δ-subharmonic functions of the nonintegral order
It is proved that the lower types of functions $T (r, u)$ and $N (r, u) = N (r, u_1) - N (z, u_2)$ relative to the proximate order $\rho(r)$ of a function $u=u_1-u_2$ of fractional order $\rho$  $δ$-subharmonic in $\mathbb {R}^m$, $m\geq2$, coincide, that is, are simultaneously minimal...
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| Date: | 1992 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
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Institute of Mathematics, NAS of Ukraine
1992
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/8182 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512961835040768 |
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| author | Zabolotsky , M. V. Заболоцький , М. В. |
| author_facet | Zabolotsky , M. V. Заболоцький , М. В. |
| author_sort | Zabolotsky , M. V. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-02-26T13:58:10Z |
| description | It is proved that the lower types of functions $T (r, u)$ and $N (r, u) = N (r, u_1) - N (z, u_2)$ relative to the proximate order $\rho(r)$ of a function $u=u_1-u_2$ of fractional order $\rho$  $δ$-subharmonic in $\mathbb {R}^m$, $m\geq2$, coincide, that is, are simultaneously minimal or mean. In the case of an arbitrary proximate order $\rho(r)$ the assertion is, in general, false. |
| first_indexed | 2026-03-24T03:37:06Z |
| format | Article |
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| id | umjimathkievua-article-8182 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T03:37:06Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/1c/d06a275075e08363123fb24d02e1391c.pdf |
| spelling | umjimathkievua-article-81822024-02-26T13:58:10Z Lower types of δ-subharmonic functions of the nonintegral order Про нижні типи δ-субгармонічних функцій нецілого порядку Zabolotsky , M. V. Заболоцький , М. В. - It is proved that the lower types of functions $T (r, u)$ and $N (r, u) = N (r, u_1) - N (z, u_2)$ relative to the proximate order $\rho(r)$ of a function $u=u_1-u_2$ of fractional order $\rho$  $δ$-subharmonic in $\mathbb {R}^m$, $m\geq2$, coincide, that is, are simultaneously minimal or mean. In the case of an arbitrary proximate order $\rho(r)$ the assertion is, in general, false. Показано, что нижние типы функций $T(r, u)$ и $N (r, u) = N (r, u_1) - N (z, u_2)$  относительно уточненного порядка $\rho(r)$  $δ$-субгармонической в $\mathbb {R}^m$, $m\geq2$, функции $u=u_1-u_2$ нецелого порядка $\rho$  совпадают, т. е. одновременно минимальны или средние. В случае произвольного уточненного порядка $\rho(r)$ утверждение, вообще говоря, ложно. Показано, що нижні типи функцій $T (r, u)$ і $N (r, u) = N (r, u_1) - N (z, u_2)$ відносно уточненого порядку $\rho(r)$ $δ$-субгармонічної в $\mathbb {R}^m$, $m\geq2$, функції $u=u_1-u_2$ нецілого порядку $\rho$ співпадають, тобто одночасно мінімальні або середні. У випадку довільного уточненого порядку $\rho(r)$ твердження, взагалі кажучи, хибне. Institute of Mathematics, NAS of Ukraine 1992-10-07 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8182 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 9 (1992); 1280-1284 Український математичний журнал; Том 44 № 9 (1992); 1280-1284 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/8182/9705 Copyright (c) 1992 M. V. Zabolotsky |
| spellingShingle | Zabolotsky , M. V. Заболоцький , М. В. Lower types of δ-subharmonic functions of the nonintegral order |
| title | Lower types of δ-subharmonic functions of the nonintegral order |
| title_alt | Про нижні типи δ-субгармонічних функцій нецілого порядку |
| title_full | Lower types of δ-subharmonic functions of the nonintegral order |
| title_fullStr | Lower types of δ-subharmonic functions of the nonintegral order |
| title_full_unstemmed | Lower types of δ-subharmonic functions of the nonintegral order |
| title_short | Lower types of δ-subharmonic functions of the nonintegral order |
| title_sort | lower types of δ-subharmonic functions of the nonintegral order |
| topic_facet | - |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8182 |
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