Reconstruction of a Pair Integral Operator of the Convolution Type
For an arbitrary operator, we pose a general reconstruction problem inverse to the problem of finding solutions. For the pair operator considered, this problem is reduced to the equivalent problem of reconstruction of the kernels of the pair integral equation of the convolution type that generates t...
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| Date: | 2002 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
2002
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/4148 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860510283874697216 |
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| author | Poletaev, G. S. Полетаев, Г. С. Полетаев, Г. С. |
| author_facet | Poletaev, G. S. Полетаев, Г. С. Полетаев, Г. С. |
| author_sort | Poletaev, G. S. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T20:23:18Z |
| description | For an arbitrary operator, we pose a general reconstruction problem inverse to the problem of finding solutions. For the pair operator considered, this problem is reduced to the equivalent problem of reconstruction of the kernels of the pair integral equation of the convolution type that generates this operator. In the cases investigated, we prove theorems that characterize the reconstruction of the corresponding kernels, which are constructed in terms of two functions from different Banach algebras of the type L 1(−∞, ∞) with weight. |
| first_indexed | 2026-03-24T02:54:33Z |
| format | Article |
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| id | umjimathkievua-article-4148 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T02:54:33Z |
| publishDate | 2002 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/db/a50e2326751ba2dcb64cd16e1fdbcadb.pdf |
| spelling | umjimathkievua-article-41482020-03-18T20:23:18Z Reconstruction of a Pair Integral Operator of the Convolution Type Восстановление парного интегрального оператора типа свертки Poletaev, G. S. Полетаев, Г. С. Полетаев, Г. С. For an arbitrary operator, we pose a general reconstruction problem inverse to the problem of finding solutions. For the pair operator considered, this problem is reduced to the equivalent problem of reconstruction of the kernels of the pair integral equation of the convolution type that generates this operator. In the cases investigated, we prove theorems that characterize the reconstruction of the corresponding kernels, which are constructed in terms of two functions from different Banach algebras of the type L 1(−∞, ∞) with weight. Для довільного опера юра поставлено загальну обернену по відношенню до пошуку розв'язків задачу відновлення. Цю задачу для розглянутого парного оператора зведено до еквівалентної задачі відновлення ядер породжуючого оператор парного ішсгралмюго рівняння чипу згортки. У вивчених випадках доведено теореми, що характеризую і ь відновлення відповідних ядер, які будуються через дві функції із різних банахових алгебр типу L 1(−∞, ∞) з вагою. Institute of Mathematics, NAS of Ukraine 2002-08-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4148 Ukrains’kyi Matematychnyi Zhurnal; Vol. 54 No. 8 (2002); 1077-1088 Український математичний журнал; Том 54 № 8 (2002); 1077-1088 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/4148/5005 https://umj.imath.kiev.ua/index.php/umj/article/view/4148/5006 Copyright (c) 2002 Poletaev G. S. |
| spellingShingle | Poletaev, G. S. Полетаев, Г. С. Полетаев, Г. С. Reconstruction of a Pair Integral Operator of the Convolution Type |
| title | Reconstruction of a Pair Integral Operator of the Convolution Type |
| title_alt | Восстановление парного интегрального оператора типа свертки |
| title_full | Reconstruction of a Pair Integral Operator of the Convolution Type |
| title_fullStr | Reconstruction of a Pair Integral Operator of the Convolution Type |
| title_full_unstemmed | Reconstruction of a Pair Integral Operator of the Convolution Type |
| title_short | Reconstruction of a Pair Integral Operator of the Convolution Type |
| title_sort | reconstruction of a pair integral operator of the convolution type |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/4148 |
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