$L^2$ restriction bounds for analytic continuations of quantum ergodic Laplace eigenfunctions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908579194208256 |
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| author | Toth, John A. Xiao, Xiao |
| author_facet | Toth, John A. Xiao, Xiao |
| contents | We prove a quantum ergodic restriction (QER) theorem for real hypersurfaces $Σ\subset X,$ where $X$ is the Grauert tube associated with a real-analytic, compact Riemannian manifold. As an application, we obtain $h$ independent upper and lower bounds for the $L^2$ - restrictions of the FBI transform of Laplace eigenfunctions restricted to $Σ$ satisfying certain generic geometric conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05570 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $L^2$ restriction bounds for analytic continuations of quantum ergodic Laplace eigenfunctions Toth, John A. Xiao, Xiao Analysis of PDEs Differential Geometry Spectral Theory We prove a quantum ergodic restriction (QER) theorem for real hypersurfaces $Σ\subset X,$ where $X$ is the Grauert tube associated with a real-analytic, compact Riemannian manifold. As an application, we obtain $h$ independent upper and lower bounds for the $L^2$ - restrictions of the FBI transform of Laplace eigenfunctions restricted to $Σ$ satisfying certain generic geometric conditions. |
| title | $L^2$ restriction bounds for analytic continuations of quantum ergodic Laplace eigenfunctions |
| topic | Analysis of PDEs Differential Geometry Spectral Theory |
| url | https://arxiv.org/abs/2510.05570 |