On divergence of series of exponents representing functions regular in convex polygons
We prove that, on a convex polygon, there exist functions from the Smirnov class E whose series of exponents diverge in the metric of the space E. Similar facts are established for the convergence almost everywhere on the boundary of a polygon, for the uniform convergence on a closed polygon, and fo...
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| Datum: | 1994 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
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Institute of Mathematics, NAS of Ukraine
1994
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/5744 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511968724516864 |
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| author | Mel'nik, Yu. I. Мельник, Ю. И. Мельник, Ю. И. |
| author_facet | Mel'nik, Yu. I. Мельник, Ю. И. Мельник, Ю. И. |
| author_sort | Mel'nik, Yu. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:16:47Z |
| description | We prove that, on a convex polygon, there exist functions from the Smirnov class E whose series of exponents diverge in the metric of the space E. Similar facts are established for the convergence almost everywhere on the boundary of a polygon, for the uniform convergence on a closed polygon, and for the pointwise convergence at noncorner points of the boundary. |
| first_indexed | 2026-03-24T03:21:19Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5744 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:21:19Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/17/ef5e11dbdda9613519aaca7c81ee1617.pdf |
| spelling | umjimathkievua-article-57442020-03-19T09:16:47Z On divergence of series of exponents representing functions regular in convex polygons О расходимости рядов экспонент, представляющих регулярные в выпуклых многоугольниках функции Mel'nik, Yu. I. Мельник, Ю. И. Мельник, Ю. И. We prove that, on a convex polygon, there exist functions from the Smirnov class E whose series of exponents diverge in the metric of the space E. Similar facts are established for the convergence almost everywhere on the boundary of a polygon, for the uniform convergence on a closed polygon, and for the pointwise convergence at noncorner points of the boundary. Доведено існування функцій класів Смирнова $E$ на опуклому многокутнику, ряди експонент яких розбігаються у метриці простору $E$. Аналогічні факти встановлені у випадку збіжності майже скрізь на межі многокутника, рівномірної збіжності на замкненому многокутнику та поточкової збіжності в некутових межових точках. Institute of Mathematics, NAS of Ukraine 1994-04-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5744 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 4 (1994); 443–445 Український математичний журнал; Том 46 № 4 (1994); 443–445 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5744/8173 https://umj.imath.kiev.ua/index.php/umj/article/view/5744/8174 Copyright (c) 1994 Mel'nik Yu. I. |
| spellingShingle | Mel'nik, Yu. I. Мельник, Ю. И. Мельник, Ю. И. On divergence of series of exponents representing functions regular in convex polygons |
| title | On divergence of series of exponents representing functions regular in convex polygons |
| title_alt | О расходимости рядов экспонент, представляющих регулярные в выпуклых многоугольниках функции |
| title_full | On divergence of series of exponents representing functions regular in convex polygons |
| title_fullStr | On divergence of series of exponents representing functions regular in convex polygons |
| title_full_unstemmed | On divergence of series of exponents representing functions regular in convex polygons |
| title_short | On divergence of series of exponents representing functions regular in convex polygons |
| title_sort | on divergence of series of exponents representing functions regular in convex polygons |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5744 |
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