On the vanishing of eigenfunctions of the Laplacian on tori
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866911163873230848 |
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| author | Germain, Pierre Moyano, Iván Zhu, Hui |
| author_facet | Germain, Pierre Moyano, Iván Zhu, Hui |
| contents | Consider an eigenfunction of the Laplacian on a torus. How small can its $L^2$-norm be on small balls? We provide partial answers to this question by exploiting the distribution of integer points on spheres, basic properties of polynomials, and Nazarov--Turán type estimates for exponential polynomials. Applications to quantum limits and control theory are given. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_19925 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the vanishing of eigenfunctions of the Laplacian on tori Germain, Pierre Moyano, Iván Zhu, Hui Analysis of PDEs Optimization and Control Consider an eigenfunction of the Laplacian on a torus. How small can its $L^2$-norm be on small balls? We provide partial answers to this question by exploiting the distribution of integer points on spheres, basic properties of polynomials, and Nazarov--Turán type estimates for exponential polynomials. Applications to quantum limits and control theory are given. |
| title | On the vanishing of eigenfunctions of the Laplacian on tori |
| topic | Analysis of PDEs Optimization and Control |
| url | https://arxiv.org/abs/2406.19925 |