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<p>In this article, we study the Schrödinger equation posed in the Euclidean space. We prove observability inequalities for measurable sets that are thick with respect to decaying densities. The proof relies on quantitative uncertainty principles adapted to decaying densities, notably those established by Shubin, Vakilian, Wolff, and Kovrijkine.</p>

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Application of Uncertainty Principles for Decaying Densities to the Observability of the Schrödinger Equation

  • 期刊论文

  • 发表日期：

    2026年8月4日

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  • Kévin Le Balc’h,
  • Jiaqi Yu

摘要

In this article, we study the Schrödinger equation posed in the Euclidean space. We prove observability inequalities for measurable sets that are thick with respect to decaying densities. The proof relies on quantitative uncertainty principles adapted to decaying densities, notably those established by Shubin, Vakilian, Wolff, and Kovrijkine.