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arXiv · 2406.19925

On the vanishing of eigenfunctions of the Laplacian on tori

Pierre Germain·Iván Moyano·Hui Zhu
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Abstract

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--Tur\'an type estimates for exponential polynomials. Applications to quantum limits and control theory are given.

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Pierre Germain, Iván Moyano, Hui Zhu. 2024-06-28. On the vanishing of eigenfunctions of the Laplacian on tori. https://arxiv.org/abs/2406.19925

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