Kolloquium des Departments Mathematik

Uniqueness, stability and single measurement recovery for the fractional Calderon problem

Referent: Dr. Angkana Rüland, MPI Leipzig
Veranstalter: Martin Burger

Abstract:
In this talk I discuss a nonlocal inverse problem, the fractional Calderon problem. This is an inverse problem for a fractional Schrödinger equation in which one seeks to recover information on an unknown potential by exterior measurements. In the talk, I address uniqueness and stability of the „infinite data problem“ as well as uniqueness and recovery from a single measurement.

These properties are based on the very strong unique continuation and approximation properties of fractional Schrödinger operators, which are of independent interest and which I also discuss in the talk.

This is based on joint work with T. Ghosh, M. Salo and G. Uhlmann.