Eigenvalue clusters for the hemisphere Laplacian with variable Robin condition
Abstract
We study the eigenvalue clusters of the Robin Laplacian on the 2-dimensional hemisphere with a variable Robin coefficient on the equator. The 'th cluster has +1 eigenvalues. We determine the asymptotic density of eigenvalues in the 'th cluster as tends to infinity. This density is given by an explicit integral involving the even part of the Robin coefficient.
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