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<p>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 [13, 12, 11]. 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.</p>

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Propagation of smallness and spectral estimates

  • 期刊论文

  • 发表日期：

    2025年7月13日

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  • Nicolas Burq,
  • Ivan Moyano

摘要

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 [13, 12, 11]. 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.