C*-algebras and inverse problem of electrodynamics

TL;DR

This paper demonstrates that boundary electromagnetic measurements in a Maxwell system on a Riemannian 3-manifold can determine a C*-algebra whose spectrum corresponds to a part of the manifold, using the BC-method.

Contribution

It introduces a novel approach linking boundary electromagnetic data to the structure of a C*-algebra in the inverse problem setting.

Findings

Boundary data determine a C*-algebra associated with the manifold.

The spectrum of this algebra is homeomorphic to a specific part of the manifold.

The part of the manifold identified depends on measurement duration.

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.