Analytic eigenbranches in the semi-classical limit

Haller, Stefan

doi:10.1007/s11785-020-01011-4

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Analytic eigenbranches in the semi-classical limit

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Haller, Stefan
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s11785-020-01011-4
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arXiv:2001.07154.pdf
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Haller_Analytic eigenbranches in the semi-classical limit_2020.pdf
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Haller, S. (2020). Analytic eigenbranches in the semi-classical limit. Complex Analysis and Operator Theory, 14(5): 52. doi:10.1007/s11785-020-01011-4.

Cite as: https://hdl.handle.net/21.11116/0000-0007-8385-E

Abstract

We consider a one parameter family of Laplacians on a closed manifold and
study the semi-classical limit of its analytically parametrized eigenvalues.
Our results are analogous to a theorem for scalar Schr\"odinger operators on
Euclidean space by Luc Hillairet and apply to geometric operators like Witten's
Laplacian associated with a Morse function.