Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces
We consider the structure of orthogonal polynomials in the space L 2(B, μ) for a probability measure μ on a Banach space B. These polynomials are described in terms of Hilbert–Schmidt kernels on the space of square-integrable linear functionals. We study the properties of functionals of this sort. C...
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| Date: | 2000 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2000
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4526 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510656328892416 |
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| author | Dorogovtsev, A. A. Дороговцев, А. А. Дороговцев, А. А. |
| author_facet | Dorogovtsev, A. A. Дороговцев, А. А. Дороговцев, А. А. |
| author_sort | Dorogovtsev, A. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:30:52Z |
| description | We consider the structure of orthogonal polynomials in the space L 2(B, μ) for a probability measure μ on a Banach space B. These polynomials are described in terms of Hilbert–Schmidt kernels on the space of square-integrable linear functionals. We study the properties of functionals of this sort. Certain probability measures are regarded as generalized functionals on the space (B, μ). |
| first_indexed | 2026-03-24T03:00:28Z |
| format | Article |
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| id | umjimathkievua-article-4526 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:00:28Z |
| publishDate | 2000 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/d9/b39f417c06785b125dc2065a5846a2d9.pdf |
| spelling | umjimathkievua-article-45262020-03-18T20:30:52Z Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces Измеримые функционалы и финитно абсолютно непрерывные меры на банаховых пространствах Dorogovtsev, A. A. Дороговцев, А. А. Дороговцев, А. А. We consider the structure of orthogonal polynomials in the space L 2(B, μ) for a probability measure μ on a Banach space B. These polynomials are described in terms of Hilbert–Schmidt kernels on the space of square-integrable linear functionals. We study the properties of functionals of this sort. Certain probability measures are regarded as generalized functionals on the space (B, μ). Розглядається структура ортогональних многочленів у просторі $L_2(B, μ)$ для ймовірнісної міри $μ$ на банаховому просторі $B$. Ці поліноми описано в термінах ядер Гільберта-Шмідта на просторі квадратично інтегровних лінійних функціоналів. Вивчаються властивості таких функціоналів. Деякі ймовірнісні міри розглядаються як узагальнені функціонали на просторі $B, μ$. Institute of Mathematics, NAS of Ukraine 2000-09-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4526 Ukrains’kyi Matematychnyi Zhurnal; Vol. 52 No. 9 (2000); 1194-1204 Український математичний журнал; Том 52 № 9 (2000); 1194-1204 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4526/5756 https://umj.imath.kiev.ua/index.php/umj/article/view/4526/5757 Copyright (c) 2000 Dorogovtsev A. A. |
| spellingShingle | Dorogovtsev, A. A. Дороговцев, А. А. Дороговцев, А. А. Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces |
| title | Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces |
| title_alt | Измеримые функционалы и финитно абсолютно непрерывные меры на банаховых пространствах |
| title_full | Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces |
| title_fullStr | Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces |
| title_full_unstemmed | Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces |
| title_short | Measurable Functionals and Finitely Absolutely Continuous Measures on Banach Spaces |
| title_sort | measurable functionals and finitely absolutely continuous measures on banach spaces |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4526 |
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