Scattering for anisotropic potentials
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866915880994078720 |
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| author | Korotyaev, Evgeny |
| author_facet | Korotyaev, Evgeny |
| contents | We consider the scattering for the operator $H=H_o+V$, where the unperturbed operator $H_o$ is not assumed to be elliptic and the potential $V$ is anisotropic. Under some conditions on $H_o$ and $V$ we show that the wave operators for $H_o, H$ exist and are complete, $H$ has no singular continuous spectrum and the eigenvalues of $H$ can accumulate only to zero. For stronger conditions on $V$ the operator $H$ has finite number of eigenvalues only. Moreover, these results are applied to the invariance principle and for time-dependent potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_21113 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scattering for anisotropic potentials Korotyaev, Evgeny Mathematical Physics We consider the scattering for the operator $H=H_o+V$, where the unperturbed operator $H_o$ is not assumed to be elliptic and the potential $V$ is anisotropic. Under some conditions on $H_o$ and $V$ we show that the wave operators for $H_o, H$ exist and are complete, $H$ has no singular continuous spectrum and the eigenvalues of $H$ can accumulate only to zero. For stronger conditions on $V$ the operator $H$ has finite number of eigenvalues only. Moreover, these results are applied to the invariance principle and for time-dependent potentials. |
| title | Scattering for anisotropic potentials |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2603.21113 |