We provide a simple and short proof of a multidimensional Borg-Levinson type theorem. Precisely, we prove that the knowledge of spectral boundary data determine uniquely the corresponding potential appearing in the Schödinger operator on an admissible Riemannian manifold. We also sketch the proof of uniqueness in the case of incomplete spectral boundary data. The new results in the present work complete those existing in the literature.

中文翻译：

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多维Borg-Levinson型定理的简单证明

我们提供了多维Bo​​rg-Levinson型定理的简单证明。精确地，我们证明了光谱边界数据的知识唯一确定了在可允许的黎曼流形上出现在Schödinger算子中的相应电势。我们还绘制了在光谱边界数据不完整的情况下唯一性的证明。本工作中的新结果完善了文献中已有的结果。