Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space $C_w^0$
For an arbitrary function $w:\mathbb{R} \to \left[ {0,1} \right]$, we determine the general form of a linear continuous functional on the space $C_w^0$. The criterion for denseness of polynomials in the space $L_2 \left( {\mathbb{R},d\mu } \right)$ established by Hamburger in 1921 is extended to...
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| Дата: | 2002 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
2002
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/4099 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510233136201728 |
|---|---|
| author | Bakan, A. G. Бакан, А. Г. Бакан, А. Г. |
| author_facet | Bakan, A. G. Бакан, А. Г. Бакан, А. Г. |
| author_sort | Bakan, A. G. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:22:32Z |
| description | For an arbitrary function $w:\mathbb{R} \to \left[ {0,1} \right]$, we determine the general form of a linear continuous functional on the space $C_w^0$. The criterion for denseness of polynomials in the space $L_2 \left( {\mathbb{R},d\mu } \right)$ established by Hamburger in 1921 is extended to the spaces $C_w^0$. |
| first_indexed | 2026-03-24T02:53:44Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-4099 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:53:44Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/5f/3b62528cb6026b9db9da29b86dfb0b5f.pdf |
| spelling | umjimathkievua-article-40992020-03-18T20:22:32Z Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space $C_w^0$ Критерий полиномиальной плотности и общий вид линейного непрерывного функционала на пространстве $C_w^0$ Bakan, A. G. Бакан, А. Г. Бакан, А. Г. For an arbitrary function $w:\mathbb{R} \to \left[ {0,1} \right]$, we determine the general form of a linear continuous functional on the space $C_w^0$. The criterion for denseness of polynomials in the space $L_2 \left( {\mathbb{R},d\mu } \right)$ established by Hamburger in 1921 is extended to the spaces $C_w^0$. Для довільної функції $w:\mathbb{R} \to \left[ {0,1} \right]$ знайдено загальний вигляд лінійного неперервного функціонала на просторі Встановлений Г. Гамбургером у 1921 р. критерій щільності многочленів у просторі $L_2 \left( {\mathbb{R},d\mu } \right)$ поширено на простори $C_w^0$. Institute of Mathematics, NAS of Ukraine 2002-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4099 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 5 (2002); 610-622 Український математичний журнал; Том 54 № 5 (2002); 610-622 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4099/4907 https://umj.imath.kiev.ua/index.php/umj/article/view/4099/4908 Copyright (c) 2002 Bakan A. G. |
| spellingShingle | Bakan, A. G. Бакан, А. Г. Бакан, А. Г. Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space $C_w^0$ |
| title | Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space $C_w^0$ |
| title_alt | Критерий полиномиальной плотности и общий вид линейного непрерывного функционала на пространстве $C_w^0$ |
| title_full | Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space $C_w^0$ |
| title_fullStr | Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space $C_w^0$ |
| title_full_unstemmed | Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space $C_w^0$ |
| title_short | Criterion of Polynomial Denseness and General Form of a Linear Continuous Functional on the Space $C_w^0$ |
| title_sort | criterion of polynomial denseness and general form of a linear continuous functional on the space $c_w^0$ |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4099 |
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