Quantitative spectral analysis of electromagnetic scattering. II: Evolution semigroups and non-perturbative solutions

Abstract: We carry out quantitative studies on the Green operator $ \hat{\mathscr G}$ associated with the Born equation, an integral equation that models electromagnetic scattering, building the strong stability of the evolution semigroup ${\exp(-i\tau\hat{\mathscr G})|\tau\geq0} $ on polynomial compactness and the Arendt-Batty-Lyubich-V~u theorem. The strongly-stable evolution semigroup inspires our proposal of a non-perturbative method to solve the light scattering problem and improve the Born approximation.