Fixed Energy Inverse Problem for Exponentially Decreasing Potentials Gunther Uhlmann and András Vasy

Inverse Scattering for the Magnetic Schrödinger Operator

We show that fixed energy scattering measurements for the magnetic Schrödinger operator uniquely determine the magnetic field and electric potential in dimensions n ≥ 3. The magnetic potential, its first derivatives, and the electric potential are assumed to be exponentially decaying. This improves an earlier result of Eskin and Ralston [4] which considered potentials with many derivatives. The...

Conference on Inverse Problems in Honor of Gunther Uhlmann

The Inverse Problem for the Local Geodesic Ray Transform

Under a convexity assumption on the boundary we solve a local inverse problem, namely we show that the geodesic X-ray transform can be inverted locally in a stable manner; one even has a reconstruction formula. We also show that under an assumption on the existence of a global foliation by strictly convex hypersurfaces the geodesic X-ray transform is globally injective. In addition we prove sta...

Low Energy Inverse Problems in Three-body Scattering

Scattering theory is the analysis of the motion of several interacting particles. Inverse problems in scattering theory seek the answer to the question: can one determine the interactions between particles by a scattering experiment, so, for instance, does the scattering matrix, or a part of the scattering matrix, determine the interaction? The answer, and the difficulty, greatly depends on the...

A pr 2 00 4 Inverse Scattering at a Fixed Quasi – Energy for Potentials Periodic in Time ∗ Ricardo Weder

We prove that the scattering matrix at a fixed quasi–energy determines uniquely a time–periodic potential that decays exponentially at infinity. We consider potentials that for each fixed time belong to L in space. The exponent 3/2 is critical for the singularities of the potential in space. For this singular class of potentials the result is new even in the time–independent case, where it was ...