Paley-Wiener methods in inverse spectral theory

Christer Bennewitz Dept of Mathematics, Lund University

A new method for obtaining uniqueness theorems in inverse spectral theory is described. It is based on a generalization of the classical Paley-Wiener theorem for the Fourier transform to the generalized Fourier transforms occuring in the spectral theory of differential operators. Several situations where this method has been successful will be described.