Modified Jost solutions of Schrödinger operators with locally $H^{-1}$ potentials
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866909211717271552 |
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| author | Lukić, Milivoje Wang, Xingya |
| author_facet | Lukić, Milivoje Wang, Xingya |
| contents | We study Jost solutions of Schrödinger operators with potentials which decay with respect to a local $H^{-1}$ Sobolev norm; in particular, we generalize to this setting the results of Christ--Kiselev for potentials between the integrable and square-integrable rates of decay, proving existence of solutions with WKB asymptotic behavior on a large set of positive energies. This applies to new classes of potentials which are not locally integrable, or have better decay properties with respect to the $H^{-1}$ norm due to rapid oscillations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_17715 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Modified Jost solutions of Schrödinger operators with locally $H^{-1}$ potentials Lukić, Milivoje Wang, Xingya Spectral Theory 34L40 (Primary) 35J10 (Secondary) We study Jost solutions of Schrödinger operators with potentials which decay with respect to a local $H^{-1}$ Sobolev norm; in particular, we generalize to this setting the results of Christ--Kiselev for potentials between the integrable and square-integrable rates of decay, proving existence of solutions with WKB asymptotic behavior on a large set of positive energies. This applies to new classes of potentials which are not locally integrable, or have better decay properties with respect to the $H^{-1}$ norm due to rapid oscillations. |
| title | Modified Jost solutions of Schrödinger operators with locally $H^{-1}$ potentials |
| topic | Spectral Theory 34L40 (Primary) 35J10 (Secondary) |
| url | https://arxiv.org/abs/2405.17715 |