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arxiv: math/9801090 · v3 · submitted 1998-01-20 · 🧮 math.AP · math.DG

Bounds on the multiplicity of eigenvalues for fixed membranes

Thomas Hoffman-Ostenhof , Peter W. Michor , Nikolai Nadirashvili This is my paper
classification 🧮 math.AP math.DG
keywords greatermultiplicityactuallyboundseigenvalueeigenvaluesfixedhere
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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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