Global hypoellipticity on time-periodic Gelfand-Shilov spaces via non-discrete Fourier analysis
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| Format: | Preprint |
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2025
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| author | Kowacs, André Pedroso Tokoro, Pedro Meyer |
| author_facet | Kowacs, André Pedroso Tokoro, Pedro Meyer |
| contents | In this paper, we provide a characterization of the time-periodic Gelfand-Shilov spaces, as introduced by F. de Ávila Silva and M. Cappiello [J. Funct. Anal., 282(9):29, 2022], through the asymptotic behaviour of both the Euclidean and periodic partial Fourier transforms of their elements. As an application, we establish necessary and sufficient conditions for global regularity -- within this framework -- for a broad class of constant-coefficient differential operators, as well as for first-order tube-type operators. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_13475 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global hypoellipticity on time-periodic Gelfand-Shilov spaces via non-discrete Fourier analysis Kowacs, André Pedroso Tokoro, Pedro Meyer Analysis of PDEs Primary 35B65, 42B05, Secondary 46F05 In this paper, we provide a characterization of the time-periodic Gelfand-Shilov spaces, as introduced by F. de Ávila Silva and M. Cappiello [J. Funct. Anal., 282(9):29, 2022], through the asymptotic behaviour of both the Euclidean and periodic partial Fourier transforms of their elements. As an application, we establish necessary and sufficient conditions for global regularity -- within this framework -- for a broad class of constant-coefficient differential operators, as well as for first-order tube-type operators. |
| title | Global hypoellipticity on time-periodic Gelfand-Shilov spaces via non-discrete Fourier analysis |
| topic | Analysis of PDEs Primary 35B65, 42B05, Secondary 46F05 |
| url | https://arxiv.org/abs/2506.13475 |