Mikko Salo
University of Helsinki, Finland
Date: March 8, 2005
We consider the inverse problem of recovering a magnetic field and electric potential from boundary measurements related to the stationary magnetic Schrödinger operator. The boundary measurements are given by the Dirichlet-to-Neumann map.
This will be the first
of two talks. In the first talk I will discuss weighted
parameter-dependent 
estimates for the magnetic Schrödinger
operator. The proof of the estimates is based on semiclassical
pseudodifferential calculus. In the second talk in April I will
discuss how to use these estimates to construct exponentially
growing solutions to the magnetic Schrödinger equation, and how to
use the solutions to reconstruct the magnetic field by inverting a
certain nonlinear Fourier transform.