Equivalence of classical and quantum completeness for real principal type operators on the circle
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866909273905168384 |
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| author | Taira, Kouichi |
| author_facet | Taira, Kouichi |
| contents | In this article, we prove that the completeness of the Hamilton flow and essential self-adjointness are equivalent for real principal type operators on the circle. Moreover, we study spectral properties of these operators. The proof is based on the construction of eigenfunctions with non-real eigenvalues which is well-known in scattering theory. Moreover, the relationship between scattering theory and the essential self-adjointness is explained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_07547 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Equivalence of classical and quantum completeness for real principal type operators on the circle Taira, Kouichi Analysis of PDEs Mathematical Physics 35S05, 81Q10 In this article, we prove that the completeness of the Hamilton flow and essential self-adjointness are equivalent for real principal type operators on the circle. Moreover, we study spectral properties of these operators. The proof is based on the construction of eigenfunctions with non-real eigenvalues which is well-known in scattering theory. Moreover, the relationship between scattering theory and the essential self-adjointness is explained. |
| title | Equivalence of classical and quantum completeness for real principal type operators on the circle |
| topic | Analysis of PDEs Mathematical Physics 35S05, 81Q10 |
| url | https://arxiv.org/abs/2004.07547 |