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arXiv · 2411.16984

Eigenvalue bounds for Schr\"odinger operators with complex potentials on compact manifolds

Jean-Claude Cuenin
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Abstract

We prove eigenvalue bounds for Schr\"odinger operator $-\Delta_g+V$ on compact manifolds with complex potentials $V$. The bounds depend only on an $L^q$-norm of the potential, and they are shown to be optimal, in a certain sense, on the round sphere and more general Zoll manifolds. These bounds are natural analogues of Frank's \cite{MR2820160} results in the Euclidean case.

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Jean-Claude Cuenin. 2024-11-25. Eigenvalue bounds for Schr\"odinger operators with complex potentials on compact manifolds. https://doi.org/10.1515/forum-2024-0564

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