From resolvent expansions at zero to long time wave expansions
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909618258575360 |
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| author | Christiansen, T. J. Datchev, K. Yang, M. |
| author_facet | Christiansen, T. J. Datchev, K. Yang, M. |
| contents | We prove a general abstract theorem deducing wave expansions as time goes to infinity from resolvent expansions as energy goes to zero, under an assumption of polynomial boundedness of the resolvent at high energy. We give applications to obstacle scattering, to Aharonov--Bohm Hamiltonians, to scattering in a sector, and to scattering by a compactly supported potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_03234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | From resolvent expansions at zero to long time wave expansions Christiansen, T. J. Datchev, K. Yang, M. Analysis of PDEs Mathematical Physics Spectral Theory We prove a general abstract theorem deducing wave expansions as time goes to infinity from resolvent expansions as energy goes to zero, under an assumption of polynomial boundedness of the resolvent at high energy. We give applications to obstacle scattering, to Aharonov--Bohm Hamiltonians, to scattering in a sector, and to scattering by a compactly supported potential. |
| title | From resolvent expansions at zero to long time wave expansions |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory |
| url | https://arxiv.org/abs/2408.03234 |