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Propagation of smallness and spectral estimates

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arxiv 2109.06654 v1 pith:I25C3BST submitted 2021-09-14 math.AP

Nicolas Burq (AGM - UMR 8088) , Iván Moyano (DPMMS) This is my paper · ORCID
classification math.AP
keywords estimatesspectralconsequencesprojectorpropagationsmallnessarticleclassical
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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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  1. Spectral inequalities for Schr\"odinger equations and quantitative propagation of smallness in the plane

    math.AP 2025-05 accept novelty 7.0 of 10

    The paper establishes new spectral inequalities for one-dimensional Schrödinger operators with growing potentials, with explicit exponents for thick and generalized thick sensor sets, based on a new quantitative Cauch...

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