A Theorem of Paley-Wiener Type for Schr\"odinger Evolutions
  We prove unique continuation principles for solutions of evolution Schr\"odinger equations with time dependent potentials. These correspond to uncertainly principles of Paley-Wiener type for the Fourier transform. Our results extends to a large class of semi-linear Schr\"odinger equation. 
Carlos E. Kenig, Gustavo Ponce and Luis Vega
math.AP