A simple criterion for essential self-adjointness of Weyl pseudodifferential operators
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866910965087338496 |
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| author | Fulsche, Robert van Luijk, Lauritz |
| author_facet | Fulsche, Robert van Luijk, Lauritz |
| contents | We prove a new criterion for the essential self-adjointness of pseudodifferential operators that does not involve ellipticity-type assumptions. For example, we show that self-adjointness holds in case the symbol is $C^{2d+3}$ with derivatives of order two and higher being uniformly bounded. These results also apply to hermitian operator-valued symbols on infinite-dimensional Hilbert spaces, which are important to applications in physics. Our method relies on a phase space differential calculus for quadratic forms on $L^2(\mathbb{R}^d)$, Calderón-Vaillancourt type theorems, and a recent self-adjointness result for Toeplitz operators on the Segal-Bargmann space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07153 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A simple criterion for essential self-adjointness of Weyl pseudodifferential operators Fulsche, Robert van Luijk, Lauritz Mathematical Physics Functional Analysis 47G30, 47B25, 81Q10 We prove a new criterion for the essential self-adjointness of pseudodifferential operators that does not involve ellipticity-type assumptions. For example, we show that self-adjointness holds in case the symbol is $C^{2d+3}$ with derivatives of order two and higher being uniformly bounded. These results also apply to hermitian operator-valued symbols on infinite-dimensional Hilbert spaces, which are important to applications in physics. Our method relies on a phase space differential calculus for quadratic forms on $L^2(\mathbb{R}^d)$, Calderón-Vaillancourt type theorems, and a recent self-adjointness result for Toeplitz operators on the Segal-Bargmann space. |
| title | A simple criterion for essential self-adjointness of Weyl pseudodifferential operators |
| topic | Mathematical Physics Functional Analysis 47G30, 47B25, 81Q10 |
| url | https://arxiv.org/abs/2304.07153 |