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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.15974 |
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| _version_ | 1866908719822929920 |
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| author | Kowacs, André Pedroso Silva, Marielle Aparecida |
| author_facet | Kowacs, André Pedroso Silva, Marielle Aparecida |
| contents | We develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as $(θ, T)$-periodic functions, and prove several properties and inequalities related to the Fourier transform, including a type of Poincaré inequality, which extend the periodic case. As an application, we employ this analysis to show that a continuous linear operator acting on smooth $(θ, T)$-periodic functions is globally hypoelliptic/solvable if and only if the corresponding operator which acts on periodic functions is globally hypoelliptic/solvable, and characterize the global hypoellipticity/solvability of a class of first order differential operators acting on the set of smooth $(θ, T)$-periodic functions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_15974 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Fourier analysis for $(θ,T)$-periodic functions and applications Kowacs, André Pedroso Silva, Marielle Aparecida Analysis of PDEs Primary 42A75, 42C99, Secondary 42B37, 42B05, 35B65 We develop a Fourier analysis for a generalization of the class of periodic functions, often referred to as $(θ, T)$-periodic functions, and prove several properties and inequalities related to the Fourier transform, including a type of Poincaré inequality, which extend the periodic case. As an application, we employ this analysis to show that a continuous linear operator acting on smooth $(θ, T)$-periodic functions is globally hypoelliptic/solvable if and only if the corresponding operator which acts on periodic functions is globally hypoelliptic/solvable, and characterize the global hypoellipticity/solvability of a class of first order differential operators acting on the set of smooth $(θ, T)$-periodic functions. |
| title | A Fourier analysis for $(θ,T)$-periodic functions and applications |
| topic | Analysis of PDEs Primary 42A75, 42C99, Secondary 42B37, 42B05, 35B65 |
| url | https://arxiv.org/abs/2512.15974 |