Semiclassical $L^p$ quasimode restriction estimates in two dimensions
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916137705406464 |
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| author | Oh, Sewook Ryu, Jaehyeon |
| author_facet | Oh, Sewook Ryu, Jaehyeon |
| contents | We establish the $L^p$ restriction estimates for quasimodes on a smooth curve in two dimensions. Our estimates are sharp for all smooth curves. As an application, we address $L^p$ eigenfunction restriction estimates for Laplace-Beltrami eigenfunctions on $2$-dimensional compact Riemannian manifolds without boundary and Hermite functions on $\mathbb R^2$. Our method involves a geometric analysis of the contact order between the curve and the bicharacteristic flow of the semiclassical pseudodifferential operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_16881 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Semiclassical $L^p$ quasimode restriction estimates in two dimensions Oh, Sewook Ryu, Jaehyeon Analysis of PDEs Classical Analysis and ODEs Spectral Theory 35PXX, 35SXX We establish the $L^p$ restriction estimates for quasimodes on a smooth curve in two dimensions. Our estimates are sharp for all smooth curves. As an application, we address $L^p$ eigenfunction restriction estimates for Laplace-Beltrami eigenfunctions on $2$-dimensional compact Riemannian manifolds without boundary and Hermite functions on $\mathbb R^2$. Our method involves a geometric analysis of the contact order between the curve and the bicharacteristic flow of the semiclassical pseudodifferential operator. |
| title | Semiclassical $L^p$ quasimode restriction estimates in two dimensions |
| topic | Analysis of PDEs Classical Analysis and ODEs Spectral Theory 35PXX, 35SXX |
| url | https://arxiv.org/abs/2401.16881 |