Eigenvalue distributions and Weyl laws for semi-classical non-self-adjoint operators in 2 dimensions

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dc.creatorSjoestrand, Johannes
dc.date2008-04-25
dc.date.accessioned2026-07-07T09:35:17Z
dc.date.available2026-07-07T09:35:17Z
dc.descriptionIn this note we compare two recent results about the distribution of eigenvalues for semi-classical pseudodifferential operators in two dimensions. For classes of analytic operators A. Melin and the author obtained a complex Bohr-Sommerfeld rule, showing that the eigenvalues are situated on a distorted lattice. On the other hand, with M. Hager we showed in any dimension that Weyl asymptotics holds with probability close to 1 for small random perturbations of the operator. In both cases the eigenvalues distribute to leading order according two smooth densities and we show here that the two densities are in general different.
dc.identifierhttps://arxiv.org/abs/0804.4052
dc.identifierhttp://arxiv.org/abs/0804.4052
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/159781
dc.subjectSpectral Theory
dc.subjectAnalysis of PDEs
dc.subject35P20
dc.titleEigenvalue distributions and Weyl laws for semi-classical non-self-adjoint operators in 2 dimensions
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