Bounds on the multiplicity of eigenvalues for fixed membranes

Details Bounds on the multiplicity of eigenvalues for fixed membranes Bounds on the multiplicity of eigenvalues for fixed membranes

1998-01-20

arxiv.org/abs/math/9801090v3

Geometric And Functional Analysis (GAFA). Vol. 9 (1999), 1169-1188

Mathematics

Analysis of PDEs

AmSTeX, epsf.tex, 17 encapsulated postscript figures, 17 pages. Third version with minor stylistic improvements

Scientific paper

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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