Restriction of Schrödinger eigenfunctions to submanifolds
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866918145161166848 |
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| author | Huang, Xiaoqi Wang, Xing Zhang, Cheng |
| author_facet | Huang, Xiaoqi Wang, Xing Zhang, Cheng |
| contents | For Schrödinger operators $H_V=-Δ_g+V$ with critically singular potentials $V$ on compact manifolds, we prove sharp estimates for the restriction of eigenfunctions to submanifolds. Our method refines the perturbative argument by Blair-Sire-Sogge and enables us to deal with submanifolds of all codimensions. As applications, we obtain improved estimates on negatively curved manifolds and flat tori. In particular, we extend the uniform $L^2$ restriction estimates on flat tori by Bourgain-Rudnick to singular potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_01947 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Restriction of Schrödinger eigenfunctions to submanifolds Huang, Xiaoqi Wang, Xing Zhang, Cheng Analysis of PDEs Classical Analysis and ODEs Spectral Theory 58J50, 35P99, 47A75, 47A55 For Schrödinger operators $H_V=-Δ_g+V$ with critically singular potentials $V$ on compact manifolds, we prove sharp estimates for the restriction of eigenfunctions to submanifolds. Our method refines the perturbative argument by Blair-Sire-Sogge and enables us to deal with submanifolds of all codimensions. As applications, we obtain improved estimates on negatively curved manifolds and flat tori. In particular, we extend the uniform $L^2$ restriction estimates on flat tori by Bourgain-Rudnick to singular potentials. |
| title | Restriction of Schrödinger eigenfunctions to submanifolds |
| topic | Analysis of PDEs Classical Analysis and ODEs Spectral Theory 58J50, 35P99, 47A75, 47A55 |
| url | https://arxiv.org/abs/2408.01947 |