Observability of the electropotential on a nested cylindrical domain. I. the continuous solution

摘要

The problem of observability of a dynamical system that is governed by a partial differential equation is considered. The problem is formulated under the assumption of an idealized geometry: coaxial cylinders representing the human torso and cardiac surface. An analytical solution in the form of generalized Fourier series is obtained under this assumption. This problem arises in the determination of the electropotential of the epicardial surface from discrete measurements on the torso.