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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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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: http://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.