Title: Weyl calculus with respect to the Gaussian measure and Lp-Lq boundedness of the Ornstein-Uhlenbeck semigroup in complex time
Abstract:
We show how the ``Schrödinger picture'' in quantum mechanics can be used to introduce a Weyl functional calculus for the Ornstein-Uhlenbeck operator L = -Delta + x\cdot \nabla$. It allows us to obtain simple proofs of a number of celebrated results concerning this operator. This is joint work with Pierre Portal (ANU, Canberra).