Events
DMS Applied and Computational Mathematics Seminar |
| Time: Nov 15, 2024 (02:00 PM) |
| Location: ZOOM |
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Details: Speaker: Patrizio Bifulco (FernUniversität in Hagen, Germany)
Title: Comparing the spectrum of Schrodinger operators on metric graphs using heat kernels
Abstract: We study Schrodinger operators on compact finite metric graphs subject to \(\delta\)-coupling and standard boundary conditions often known as Kirchoff-Neumann vertex conditions. We compare the \(n\)-th eigenvalues of those self-adjoint realizations and derive an asymptotic result for the mean value of the eigenvalue deviations which represents a generalization to a recent result by Rudnick, Wigman and Yesha obtained for domains in \(\mathbb{R}^2\) to the setting of metric graphs. We start this talk by introducing the basic notion of a metric graph and discuss some basic properties of heat kernels on those graphs afterwards. In this way, we are able to discuss a so-called local Weyl law which is relevant for the proof of the asymptotic main result. If time permits, we will also briefly discuss the case of \(\delta'\)-coupling conditions and some possible generalizations on infinite graphs having finite total length.
This talk is based on joint works with Joachim Kerner (Hagen) and Delio Mugnolo (Hagen).
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