Laplace-eigenfunctions on the torus with high vanishing order

Matthias Täufer

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arXiv · 1710.09328

Laplace-eigenfunctions on the torus with high vanishing order

Matthias Täufer

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Abstract

We use the sum-of-squares theorem from number theory to construct eigenfunctions of the Laplacian on the $d$-dimensional torus, $d \geq 2$, which vanish to any prescribed order at some point. These functions are then applied to provide a negative answer (in dimension $d \geq 2$) to a question in the context of quantitative unique continuation for spectral projectors of Schr\"odinger operators, asked by Egidi and Veseli\'c.

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Matthias Täufer. 2017-10-25. Laplace-eigenfunctions on the torus with high vanishing order. https://arxiv.org/abs/1710.09328

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