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arXiv · 2309.07044

Eigenvalue clusters for the hemisphere Laplacian with variable Robin condition

Alexander Pushnitski·Igor Wigman
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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.

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Alexander Pushnitski, Igor Wigman. 2023-09-13. Eigenvalue clusters for the hemisphere Laplacian with variable Robin condition. https://doi.org/10.2140/pmp.2025.6.81

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