Equivalence of time-domain inverse problems and boundary spectral problems

We consider inverse problems for wave, heat and Schrodinger-type operators and the corresponding spectral problems on domains of R-n and compact manifolds. In particular, we study the inverse problems when the measured data is the total energy flux through the boundary, that is, one knows how much energy is needed to force the solution to have given boundary values. The main result of the paper is to show that all the problems are equivalent.