Szego-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Carleman-type relations
In view of the well-known Szego - Kolmogorov - Krein theorems on weighted approximation by the functions with semibounded spectrum (on a circle or a line), an efficient construction is suggested, which enables one to realize these approximations. It is based on relations similar to the Carleman to...
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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/5773 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512000852885504 |
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| author | Bart, V. A. Khavin, V. P. Барт, В. А. Хавин, В. П. Барт, В. А. Хавин, В. П. |
| author_facet | Bart, V. A. Khavin, V. P. Барт, В. А. Хавин, В. П. Барт, В. А. Хавин, В. П. |
| author_sort | Bart, V. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:17:37Z |
| description | In view of the well-known Szego - Kolmogorov - Krein theorems on weighted approximation by the functions with semibounded spectrum (on a circle or a line),
an efficient construction is suggested, which enables one to realize these approximations.
It is based on relations similar to the Carleman tor-mula reconstructing an analytic function in terms its trace on the boundary of the domain of definition. |
| first_indexed | 2026-03-24T03:21:50Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5773 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:21:50Z |
| publishDate | 1994 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/87/d3110bd3066cba3d7ee5df3824b11b87.pdf |
| spelling | umjimathkievua-article-57732020-03-19T09:17:37Z Szego-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Carleman-type relations Теоремы Сеге - Колмогорова - Крейна о весовой тригонометрической аппроксимации и формулы карлемановского типа Bart, V. A. Khavin, V. P. Барт, В. А. Хавин, В. П. Барт, В. А. Хавин, В. П. In view of the well-known Szego - Kolmogorov - Krein theorems on weighted approximation by the functions with semibounded spectrum (on a circle or a line), an efficient construction is suggested, which enables one to realize these approximations. It is based on relations similar to the Carleman tor-mula reconstructing an analytic function in terms its trace on the boundary of the domain of definition. У світлі відомих теорем Г. Сеге, А. М. Колмогорова та М. Г. Крейна про вагове наближення функціями з напівобмеженим спектром (на колі та прямій) запропонована ефективна конструкція, іцо реалізує такі наближення. Вона заснована на формулах типу формули Карлемана, що відновлює аналітичну функцію за її слідом на границі області задания. Institute of Mathematics, NAS of Ukraine 1994-02-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5773 Ukrains’kyi Matematychnyi Zhurnal; Vol. 46 No. 1-2 (1994); 100–127 Український математичний журнал; Том 46 № 1-2 (1994); 100–127 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5773/8230 https://umj.imath.kiev.ua/index.php/umj/article/view/5773/8231 Copyright (c) 1994 Bart V. A.; Khavin V. P. |
| spellingShingle | Bart, V. A. Khavin, V. P. Барт, В. А. Хавин, В. П. Барт, В. А. Хавин, В. П. Szego-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Carleman-type relations |
| title | Szego-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Carleman-type relations |
| title_alt | Теоремы Сеге - Колмогорова - Крейна о весовой тригонометрической аппроксимации и формулы карлемановского типа |
| title_full | Szego-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Carleman-type relations |
| title_fullStr | Szego-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Carleman-type relations |
| title_full_unstemmed | Szego-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Carleman-type relations |
| title_short | Szego-Kolmogorov-Krein theorems on weighted trigonometrical approximation and Carleman-type relations |
| title_sort | szego-kolmogorov-krein theorems on weighted trigonometrical approximation and carleman-type relations |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5773 |
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