Global solvability for a class of pseudodifferential operators on the torus
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866909277944283136 |
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| author | Ferra, Igor A. |
| author_facet | Ferra, Igor A. |
| contents | We give a complete characterization for the global solvability of a pseudodifferential operator P=D_t + c(t,D_x) on the (N+1)-dimensional torus T^{N+1} = S^1_t x T^N_x. Our characterization is given in terms of diophantine conditions and a notion of super-logarithmic oscilation of the symbol of the imaginary part of c(t,D_x). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01183 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global solvability for a class of pseudodifferential operators on the torus Ferra, Igor A. Analysis of PDEs We give a complete characterization for the global solvability of a pseudodifferential operator P=D_t + c(t,D_x) on the (N+1)-dimensional torus T^{N+1} = S^1_t x T^N_x. Our characterization is given in terms of diophantine conditions and a notion of super-logarithmic oscilation of the symbol of the imaginary part of c(t,D_x). |
| title | Global solvability for a class of pseudodifferential operators on the torus |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.01183 |