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Bounds on the multiplicity of eigenvalues for fixed membranes

Thomas Hoffman-Ostenhof·Peter W. Michor·Nikolai Nadirashvili
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Abstract

For a membrane in the plane the multiplicity of the $k$-th eigenvalue is known to be not greater than $2k-1$. Here we prove that it is actually not greater than $2k-3$, for $k\ge 3$.

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Thomas Hoffman-Ostenhof, Peter W. Michor, Nikolai Nadirashvili. 1999-06-02. Bounds on the multiplicity of eigenvalues for fixed membranes. https://arxiv.org/abs/math/9801090

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