Iryna Egorova and Gerald Teschl
A Paley-Wiener Theorem for Periodic Scattering with Applications to the Korteweg-de Vries Equation
(29K, LaTeX2e)
ABSTRACT. Consider a one-dimensional Schr\"odinger operator which is a short range perturbation
of a finite-gap operator. We give necessary and sufficient conditions on the left, right reflection
coefficient such that the difference of the potentials has finite support to the left, right, respectively.
Moreover, we apply these results to show a unique continuation type result for solutions
of the Korteweg--de Vries equation in this context. By virtue of the Miura transform an
analogous result for the modified Korteweg--de Vries equation is also obtained.