Sharp Spectral-Cluster Restriction Bounds for Orthonormal Systems
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866912396037062656 |
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| author | Jian, Changbiao Wang, Xing Xi, Yakun |
| author_facet | Jian, Changbiao Wang, Xing Xi, Yakun |
| contents | For a smooth $k$-dimensional submanifold $Σ$ of a $d$-dimensional compact Riemannian manifold $M$, we extend the $L^p(Σ)$ restriction bounds of Burq-Gérard-Tzvetkov -- originally proved for individual Laplace--Beltrami eigenfunction -- to arbitrary systems of $L^2(M)$-orthonormal functions. Our bounds are essentially optimal for every triple $(k,d,p)$ with $p\ge2$, except possibly when $ d\ge3,\quad k=d-1,\quad 2\le p\le4. $ This work is inspired by a work of Frank and Sabin, who established analogous $L^p(M)$ bounds for $L^2(M)$-orthonormal systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_20657 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sharp Spectral-Cluster Restriction Bounds for Orthonormal Systems Jian, Changbiao Wang, Xing Xi, Yakun Analysis of PDEs Spectral Theory For a smooth $k$-dimensional submanifold $Σ$ of a $d$-dimensional compact Riemannian manifold $M$, we extend the $L^p(Σ)$ restriction bounds of Burq-Gérard-Tzvetkov -- originally proved for individual Laplace--Beltrami eigenfunction -- to arbitrary systems of $L^2(M)$-orthonormal functions. Our bounds are essentially optimal for every triple $(k,d,p)$ with $p\ge2$, except possibly when $ d\ge3,\quad k=d-1,\quad 2\le p\le4. $ This work is inspired by a work of Frank and Sabin, who established analogous $L^p(M)$ bounds for $L^2(M)$-orthonormal systems. |
| title | Sharp Spectral-Cluster Restriction Bounds for Orthonormal Systems |
| topic | Analysis of PDEs Spectral Theory |
| url | https://arxiv.org/abs/2505.20657 |