Journal of Operator Theory

Volume 77, Issue 1, Winter 2017  pp. 133-147.

Poisson wave trace formula for perturbed Dirac operator

Authors:  J. Kungsman (1) and Michael Melgaard (2)
Author institution:(1) Department of Mathematics, Uppsala University, SE-751 06 Uppsala, Sweden
(2) Department of Mathematics, University of Sussex, Brighton BN1 9QH, Great Britain

Summary: We consider self-adjoint Dirac operators $\mathbb{D}=\mathbb{D}_0 + V(x)$, where $\mathbb{D}_0$ is the free three-dimensional Dirac operator and $V(x)$ is a smooth compactly supported Hermitian matrix. We define resonances of $\mathbb{D}$ as poles of the meromorphic continuation of its cut-off resolvent. An upper bound on the number of resonances in disks, an estimate on the scattering determinant and the Lifshits--Krein trace formula then leads to a global Poisson wave trace formula for resonances of $\mathbb{D}$.

DOI: http://dx.doi.org/10.7900/jot.2016mar04.2119
Keywords: Dirac operator, resonances, Poisson wave trace