Optimal methods for specifying information in the solution of integral equations with analytic kernels
We determine the exact order of the minimum radius of information in the logarithmic scale for Fredholm integral equations of the second kind with periodic analytic kernels and free terms. We show that the information complexity of the solution of Fredholm equations with analytic kernels is greater...
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| Date: | 1996 |
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| Main Authors: | , , , |
| Format: | Article |
| Language: | Russian English |
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Institute of Mathematics, NAS of Ukraine
1996
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/5299 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860511519336300544 |
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| author | Azizov, M. Pereverzev, S. V. Азизов, М. Переверзев, С. В. Азизов, М. Переверзев, С. В. |
| author_facet | Azizov, M. Pereverzev, S. V. Азизов, М. Переверзев, С. В. Азизов, М. Переверзев, С. В. |
| author_sort | Azizov, M. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-18T21:29:48Z |
| description | We determine the exact order of the minimum radius of information in the logarithmic scale for Fredholm integral equations of the second kind with periodic analytic kernels and free terms. We show that the information complexity of the solution of Fredholm equations with analytic kernels is greater in order than the complexity of the approximation of analytic functions. This distinguishes the analytic case from the case of finite smoothness. |
| first_indexed | 2026-03-24T03:14:11Z |
| format | Article |
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| id | umjimathkievua-article-5299 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:14:11Z |
| publishDate | 1996 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/e9/58eda2215f3b02120f14f0e3214bb4e9.pdf |
| spelling | umjimathkievua-article-52992020-03-18T21:29:48Z Optimal methods for specifying information in the solution of integral equations with analytic kernels Об оптимальных способах задания информации при решении интегральных уравнений с аналитическими ядрами Azizov, M. Pereverzev, S. V. Азизов, М. Переверзев, С. В. Азизов, М. Переверзев, С. В. We determine the exact order of the minimum radius of information in the logarithmic scale for Fredholm integral equations of the second kind with periodic analytic kernels and free terms. We show that the information complexity of the solution of Fredholm equations with analytic kernels is greater in order than the complexity of the approximation of analytic functions. This distinguishes the analytic case from the case of finite smoothness. Знайдено точний порядок у логарифмічній шкалі мінімального радіусу інформації для рівнянь Фредгольма другого роду з періодичними аналітичними ядрами та вільними членами. З цього результату випливає, що інформаційна складність розв'язання рівнянь Фредгольма з аналітичними ядрами вища за порядком, ніж складність наближення аналітичних функцій. Це відрізняє аналітичний випадок від випадку скінченної гладкості. Institute of Mathematics, NAS of Ukraine 1996-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5299 Ukrains’kyi Matematychnyi Zhurnal; Vol. 48 No. 5 (1996); 656-664 Український математичний журнал; Том 48 № 5 (1996); 656-664 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5299/7290 https://umj.imath.kiev.ua/index.php/umj/article/view/5299/7291 Copyright (c) 1996 Azizov M.; Pereverzev S. V. |
| spellingShingle | Azizov, M. Pereverzev, S. V. Азизов, М. Переверзев, С. В. Азизов, М. Переверзев, С. В. Optimal methods for specifying information in the solution of integral equations with analytic kernels |
| title | Optimal methods for specifying information in the solution of integral equations with analytic kernels |
| title_alt | Об оптимальных способах задания информации при
решении интегральных уравнений с аналитическими ядрами |
| title_full | Optimal methods for specifying information in the solution of integral equations with analytic kernels |
| title_fullStr | Optimal methods for specifying information in the solution of integral equations with analytic kernels |
| title_full_unstemmed | Optimal methods for specifying information in the solution of integral equations with analytic kernels |
| title_short | Optimal methods for specifying information in the solution of integral equations with analytic kernels |
| title_sort | optimal methods for specifying information in the solution of integral equations with analytic kernels |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5299 |
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