Scattering matrix for the wave equation with finite radial potential in the two-dimensional space
Expressions for partial scattering matrices $S_l(\lambda)$ are obtained for all naturall by using Adamyan's result, which establishes a universal relationship between the scattering matrix for the wave equation with finite potential in a even-dimensional space and the characteristic operato...
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| Дата: | 1993 |
|---|---|
| Автори: | , |
| Формат: | Стаття |
| Мова: | Російська Англійська |
| Опубліковано: |
Institute of Mathematics, NAS of Ukraine
1993
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| Онлайн доступ: | https://umj.imath.kiev.ua/index.php/umj/article/view/5868 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Репозитарії
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512088753963008 |
|---|---|
| author | Mil'man, A. L. Мильман, А. Л. Мильман, А. Л. |
| author_facet | Mil'man, A. L. Мильман, А. Л. Мильман, А. Л. |
| author_sort | Mil'man, A. L. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2020-03-19T09:19:41Z |
| description | Expressions for partial scattering matrices $S_l(\lambda)$ are obtained for all naturall by using Adamyan's result, which establishes a universal relationship between the scattering matrix for the wave equation with finite potential in a even-dimensional space and the characteristic operator function of a special contraction operator, which describes the dissipation of energy from the region of the space containing a scatterer. It is shown that this problem can be reduced to the case of $l = 0$ for all even $l$ and to the case of $l = 1$ for all odd $l$. |
| first_indexed | 2026-03-24T03:23:14Z |
| format | Article |
| fulltext |
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| id | umjimathkievua-article-5868 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | rus English |
| last_indexed | 2026-03-24T03:23:14Z |
| publishDate | 1993 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/77/0ab8910497415f32325595b52068ae77.pdf |
| spelling | umjimathkievua-article-58682020-03-19T09:19:41Z Scattering matrix for the wave equation with finite radial potential in the two-dimensional space Матрица рассеяния для волнового уравнения с финитным радиальным потенциалом в двумерном пространстве Mil'man, A. L. Мильман, А. Л. Мильман, А. Л. Expressions for partial scattering matrices $S_l(\lambda)$ are obtained for all naturall by using Adamyan's result, which establishes a universal relationship between the scattering matrix for the wave equation with finite potential in a even-dimensional space and the characteristic operator function of a special contraction operator, which describes the dissipation of energy from the region of the space containing a scatterer. It is shown that this problem can be reduced to the case of $l = 0$ for all even $l$ and to the case of $l = 1$ for all odd $l$. Одержано вирази для парціальних матриць розсіяння $S_l(\lambda)$ при будь-яких натуральних $l$ з використанням встановленого В. М. Адамяном універсального зв’язку між матрицею розсіяння для хвильового рівняння з фінітним потенціалом у парновимірному просторі та характеристичною оператор-функцією спеціального оператора стиску, що описує дисипацію енергії з області простору, що містить розсіювач. Показано, що при всіх парних $l$ задача зводиться до випадку $l = 0$, а при всіх непарних $l$—до випадку $l = 1$. Institute of Mathematics, NAS of Ukraine 1993-06-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/5868 Ukrains’kyi Matematychnyi Zhurnal; Vol. 45 No. 6 (1993); 791–802 Український математичний журнал; Том 45 № 6 (1993); 791–802 1027-3190 rus en https://umj.imath.kiev.ua/index.php/umj/article/view/5868/8419 https://umj.imath.kiev.ua/index.php/umj/article/view/5868/8420 Copyright (c) 1993 Mil'man A. L. |
| spellingShingle | Mil'man, A. L. Мильман, А. Л. Мильман, А. Л. Scattering matrix for the wave equation with finite radial potential in the two-dimensional space |
| title | Scattering matrix for the wave equation with finite radial potential in the two-dimensional space |
| title_alt | Матрица рассеяния для волнового уравнения с финитным радиальным потенциалом в двумерном пространстве |
| title_full | Scattering matrix for the wave equation with finite radial potential in the two-dimensional space |
| title_fullStr | Scattering matrix for the wave equation with finite radial potential in the two-dimensional space |
| title_full_unstemmed | Scattering matrix for the wave equation with finite radial potential in the two-dimensional space |
| title_short | Scattering matrix for the wave equation with finite radial potential in the two-dimensional space |
| title_sort | scattering matrix for the wave equation with finite radial potential in the two-dimensional space |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/5868 |
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