Friday, June 1, 2018 - 16:15 in V3-204
Upper and lower Lipschitz bounds for the perturbation of edges of the essential spectrum
A talk in the Kolloquium Mathematische Physik series by
Ivan Veselić from TU Dortmund
| Abstract: |
Let $A$ be a selfadjoint operator, $B$ a bounded symmetric operator and $A+t B$ a perturbation. I will present upper and lower Lipschitz bounds on the function of $t$ which locally describes the movement of edges of the essential spectrum. Analogous bounds apply also for eigenvalues within gaps of the essential spectrum. The bounds hold for an optimal range of values of the coupling constant $t$.
This is result is applied to Schroedinger operators on unbounded domains which are perturbed by a non-negative potential which is mostly equal to zero. Unique continuation estimates nevertheless ensure quantitative bounds on the lifting of spectral edges due to this semidefinite potential. This allows to perform spectral engineering in certain situations.
The talks is based on the preprint https://arxiv.org/abs/1804.07816
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