C*-algebras and inverse problem of electrodynamics

Abstract

We consider the dynamical inverse problem for the Maxwell system on a Riemannian 3-manifold with boundary in a time-optimal set-up. Using BC-method we show that the data of the inverse problem (electromagnetic measurements on the boundary) determine a $C$*-algebra, which has a spectrum homeomorphic to a part of the manifold. This part depends on the duration of measurements.