THE TRACE FORMULA FOR SCHRODINGER-OPERATORS FROM INFINITE-DIMENSIONALOSCILLATORY INTEGRALS

The theory of infinite dimensional oscillatory integrals by finite dim ensional approximations is shown to provide new information on the tra ce formula for Schrodinger operators. In particular, the explicit comp utation of contributions given by constant and non constant periodic o rbits, for potentials which are quadratic plus a bounded nonlinear par t, is provided. The heat semigroup as well as the Schrodinger group ar e discussed and it is shown in particular that their singular supports are contained in an explicit countable set independent of the bounded part of the potential.