03. Juni 2026
Francesco Ferraresso (Università di Verona)
An overview on the spectrum of Maxwell operators
The Maxwell system (1865) in time-harmonic formulation has always an infinite dimensional kernel, even in bounded domains; therefore, the Maxwell essential spectrum is always not-empty, and many standard spectral theory techniques fail. Even more dramatically, dissipative Maxwell systems in bounded domains might have segments of essential spectrum along the imaginary axis.
I will give a survey on some recent results regarding the spectrum of the Maxwell system. In the bounded domain case, I will show how the geometry can interact with the spectrum of a simplified Maxwell operator. In unbounded domains, the aim will be to characterise and localise the essential spectrum, and to provide a spectral approximation theorem to prove the exactness of domain truncation methods.
I will then discuss a few generalisations of these ideas to different geometric settings and to more realistic Maxwell-type systems.
Based on joint work with S. Bögli (Durham), M. Marletta (Cardiff), L. Provenzano (Sapienza Rome) and C. Tretter (Bern).