Propagation of smallness and spectral estimates

Nicolas Burq; Iván Moyano

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arXiv · 2109.06654

Propagation of smallness and spectral estimates

Nicolas Burq·Iván Moyano

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Abstract

The purpose of this article is to show that the spectral projector estimates for Laplace operators can be deduced from Logunov-Malinnikova's Propagation of smallness estimates for harmonic functions [11, 10, 9]. The main point is to pass from the local estimates obtained in [4] (on a compact manifold) to global estimates. We also state classical consequences in terms of observability and control for heat equations, which are direct consequences of these spectral projector estimates..

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Nicolas Burq, Iván Moyano. 2021-09-14. Propagation of smallness and spectral estimates. https://arxiv.org/abs/2109.06654

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