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...
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| Date: | 2026 |
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| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Institute of Mathematics, NAS of Ukraine
2026
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/1520 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | 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. |
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| DOI: | 10.3842/umzh.v71i10.1520 |