Restriction of Schrödinger eigenfunctions to submanifolds

Fuente: arXiv
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Autores principales: Huang, Xiaoqi, Wang, Xing, Zhang, Cheng
Formato: Preprint
Publicado: 2024
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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