Hokkaido University Preprint Series in Mathematics
We study analytic smoothing effect of solutions to the Schr odinger equation with Cauchy data decaying exponentially at in nity. The do- main of analyticity in the space variables of solutions is described under weight conditions on the data in the terms of the corresponding supporting functios. The domain of analyticity in the time variable is characterized by means of weight conditions of Gaussian type on the data. A general- ization of various isometrical identities related to the analytic smoothing effect is introduced.