2017

2017

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).