Smooth vectors and Weyl-Pedersen calculus for representations of nilpotent Lie groups

Abstract

We present some recent results on smooth vectors for unitary irreducible representations of nilpotent Lie groups. Applications to the Weyl-Pedersen calculus of pseudo-differential operators with symbols on the coadjoint orbits are also discussed.

The paper is dedicated to Professor Ion Colojoara for his eightieth birthday