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arXiv · 2510.05570

$L^2$ restriction bounds for analytic continuations of quantum ergodic Laplace eigenfunctions

John A. Toth·Xiao Xiao
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Abstract

We prove a quantum ergodic restriction (QER) theorem for real hypersurfaces $\Sigma \subset X,$ 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 $\Sigma$ satisfying certain generic geometric conditions.

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John A. Toth, Xiao Xiao. 2025-10-07. $L^2$ restriction bounds for analytic continuations of quantum ergodic Laplace eigenfunctions. https://arxiv.org/abs/2510.05570

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