Globally solvable time-periodic evolution equations in Gelfand-Shilov classes
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910354266652672 |
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| author | Silva, Fernando de Ávila Cappiello, Marco |
| author_facet | Silva, Fernando de Ávila Cappiello, Marco |
| contents | In this paper we consider a class of evolution operators with coefficients depending on time and space variables $(t,x) \in \mathbb{T} \times \mathbb{R}^n$, where $\mathbb{T}$ is the one-dimensional torus and prove necessary and sufficient conditions for their global solvability in (time-periodic) Gelfand-Shilov spaces. The argument of the proof is based on a characterization of these spaces in terms of the eigenfunction expansions given by a fixed self-adjoint, globally elliptic differential operator on $\mathbb{R}^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_10006 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Globally solvable time-periodic evolution equations in Gelfand-Shilov classes Silva, Fernando de Ávila Cappiello, Marco Analysis of PDEs 46F05, 35B10, 35B65, 35A01 In this paper we consider a class of evolution operators with coefficients depending on time and space variables $(t,x) \in \mathbb{T} \times \mathbb{R}^n$, where $\mathbb{T}$ is the one-dimensional torus and prove necessary and sufficient conditions for their global solvability in (time-periodic) Gelfand-Shilov spaces. The argument of the proof is based on a characterization of these spaces in terms of the eigenfunction expansions given by a fixed self-adjoint, globally elliptic differential operator on $\mathbb{R}^n$. |
| title | Globally solvable time-periodic evolution equations in Gelfand-Shilov classes |
| topic | Analysis of PDEs 46F05, 35B10, 35B65, 35A01 |
| url | https://arxiv.org/abs/2402.10006 |