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Markus Holzmann: Spectral properties of self-adjoint Dirac operators on domains in R^3

Time: Wed 2020-05-13 13.15 - 14.15

Location: Zoom, Meeting ID: 690 3199 5820

Participating: Markus Holzmann, Technische Universität Graz

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Let \(\Omega \subset \mathbb{R}^3\) be a bounded or unbounded domain with compact \(C^2\)-smooth boundary. In this talk Dirac operators acting on functions which satisfy suitable boundary conditions that yield self-adjoint operators in \(L^2(\Omega; \mathbb{C}^4)\) are discussed. Such operators are the relativistic counterparts of Laplacians on \(\Omega\) with Robin-type boundary conditions. The self-adjointness of the operators is shown for a wide class of boundary values and the basic spectral properties are investigated. It turns out that there are some critical boundary values for which the spectral properties of the corresponding operators are of a completely different nature, as it is shown with the help of an explicit example.

This talk is based on joint works with J. Behrndt and A. Mas.