Hyperbolic systems in Gelfand and Shilov spaces
UDC 517.956.32, 517.955.2 For systems hyperbolic in Shilov's sense with time-dependent coefficients, the properties of the Green function are studied in the $S$-type spaces. For systems of this kind in the indicated spaces, we establish the correct solvability of the Cauchy problem. It...
Gespeichert in:
| Datum: | 2026 |
|---|---|
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2026
|
| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/1520 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
Institution
Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1865788463600631808 |
|---|---|
| author | Litovchenko, V. A. Літовченко, В. А. |
| author_facet | Litovchenko, V. A. Літовченко, В. А. |
| author_institution_txt_mv | [
{
"author": "В. А. Літовченко",
"institution": "Чернiв. нац. ун-т"
}
] |
| author_sort | Litovchenko, V. A. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2026-02-09T14:34:17Z |
| description | UDC 517.956.32, 517.955.2
For systems hyperbolic in Shilov's sense with time-dependent coefficients, the properties of the Green function are studied in the $S$-type spaces.
For systems of this kind in the indicated spaces, we establish the correct solvability of the Cauchy problem.
It is shown that, for each $\beta>1,$ the space ${S_0^\beta}'$ of Gelfand and Shilov distributions is the class of well-posedness of this problem. |
| doi_str_mv | 10.3842/umzh.v71i10.1520 |
| first_indexed | 2026-03-24T02:07:23Z |
| format | Article |
| fulltext | |
| id | umjimathkievua-article-1520 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T02:07:23Z |
| publishDate | 2026 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | |
| spelling | umjimathkievua-article-15202026-02-09T14:34:17Z Hyperbolic systems in Gelfand and Shilov spaces Гіперболічні системи у просторах Гельфанда і Шилова Litovchenko, V. A. Літовченко, В. А. UDC 517.956.32, 517.955.2 For systems hyperbolic in Shilov's sense with time-dependent coefficients, the properties of the Green function are studied in the $S$-type spaces. For systems of this kind in the indicated spaces, we establish the correct solvability of the Cauchy problem. It is shown that, for each $\beta>1,$ the space ${S_0^\beta}'$ of Gelfand and Shilov distributions is the class of well-posedness of this problem. УДК 517.956.32, 517.955.2 Для гіперболічних за Шиловим систем із неперервно залежними від часу коефіцієнтами досліджено властивості функції Гріна у просторах типу $S.$ Для таких систем у цих просторах встановлено коректну розв'язність задачі Коші та доведено, що простір ${S_0^\beta}'$ розподілів Гельфанда і Шилова при кожному $\beta>1$ є класом коректності цієї задачі. Institute of Mathematics, NAS of Ukraine 2026-02-09 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/1520 10.3842/umzh.v71i10.1520 Ukrains’kyi Matematychnyi Zhurnal; Vol. 71 No. 10 (2019); 1360-1373 Український математичний журнал; Том 71 № 10 (2019); 1360-1373 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/1520/503 Copyright (c) 2019 Litovchenko V. A. |
| spellingShingle | Litovchenko, V. A. Літовченко, В. А. Hyperbolic systems in Gelfand and Shilov spaces |
| title | Hyperbolic systems in Gelfand and Shilov spaces |
| title_alt | Гіперболічні системи у просторах Гельфанда і Шилова |
| title_full | Hyperbolic systems in Gelfand and Shilov spaces |
| title_fullStr | Hyperbolic systems in Gelfand and Shilov spaces |
| title_full_unstemmed | Hyperbolic systems in Gelfand and Shilov spaces |
| title_short | Hyperbolic systems in Gelfand and Shilov spaces |
| title_sort | hyperbolic systems in gelfand and shilov spaces |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/1520 |
| work_keys_str_mv | AT litovchenkova hyperbolicsystemsingelfandandshilovspaces AT lítovčenkova hyperbolicsystemsingelfandandshilovspaces AT litovchenkova gíperbolíčnísistemiuprostorahgelʹfandaíšilova AT lítovčenkova gíperbolíčnísistemiuprostorahgelʹfandaíšilova |