Semiclassical $L^p$ quasimode restriction estimates in two dimensions

Sewook Oh; Jaehyeon Ryu

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arXiv · 2401.16881

Semiclassical $L^p$ quasimode restriction estimates in two dimensions

Sewook Oh·Jaehyeon Ryu

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Abstract

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.

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Sewook Oh, Jaehyeon Ryu. 2024-01-30. Semiclassical $L^p$ quasimode restriction estimates in two dimensions. https://arxiv.org/abs/2401.16881

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