Bounds on the multiplicity of eigenvalues for fixed membranes

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 $k\ge 3$.

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