The imaginary part of the scattering Green function: monochromatic relations to the real part and uniqueness results for inverse problems

Joint work with Thorsten Hohage and Roman G. Novikov

For many wave propagation problems with random sources it has been demonstrated  that cross correlations of wave fields are proportional to the imaginary part of the Green function of the underlying wave equation. This leads to the inverse problem to recover coefficients of a wave equation from the imaginary part of the Green function on some measurement manifold. 
In this talk I will speak, in particular, about local uniqueness results for the Schrödinger equation with one frequency, and for the acoustic wave equation with unknown density and sound speed and two frequencies. As the main tool of the analysis, I will present new algebraic identities between the real and the imaginary part of Green's function, which in contrast to the well-known Kramers-Kronig relations involve only one frequency.