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 $\ell$'th cluster has $\ell +1$ eigenvalues. We determine the asymptotic density of eigenvalues in the $\ell$'th cluster as $\ell$ tends to infinity. This density is given by an explicit integral involving the even part of the Robin coefficient.

32 pages, to appear in Probability and Mathematical Physics

References in corpus (1)

• Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian