Spectral properties of rational operator functions

Speaker: Christian Engström, Lund University

Abstract: Integro-differential operators are common in many areas of physics, including electromagnetics, viscoelasticity, and modeling of high-intensity ultrasound. The related operator functions share spectral properties with a linear non-selfadjoint block operator. However, the block operator is not a relatively compact perturbation of a selfadjoint operator, which makes a direct analysis of the non-selfadjoint operator challenging.

Therefore, we base our approach on factorization results for bounded holomorphic operator functions that were developed by several authors including I. Gohberg, M. Krein, H. Langer, A. S Markus, V. I. Matsaev, and G. I. Russu.

In this talk, we consider sufficient conditions for the accumulation of branches of eigenvalues to the essential spectrum and spectral enclosures. The focus is on Maxwell’s equations and the Moore-Gibson-Thompson equation with an exponentially decaying memory.