Final Report Summary - RESTRICTION (Restriction of the Fourier transform with applications to the Schrödinger and wave equations)
Electrical impedance tomography was shown to be founded in theoretically viable mathematics, provided that the objects that are being imaged are not too rough. This solved a conjecture made in the International Congress of Mathematicians in 1998. A number of inequalities were established that control the size of waves at later times in terms of their size at an initial time. Finally, an extension of the fundamental theorem of calculus, that tells us that integration is the inverse operation to differentiation, was proven in three and more dimensions.