Pseudo-Differential Operators on Heisenberg Groups

Abstract

The convalution operators on the euclidean spaces are only a particular case of convolution operators on arbitrary Lie groups. Pseudo-differential operators are roughly speaking convolution operators with variable coefficients. In classical theory of such operators it is important to have standard dilations on a euclidean space. So we pay attention only to Lie groups with dilation i.e. with 1-dimensional group of automorphisms converging to infinity when real parameter increases to infinity. It is well known that all Lie groups with dilations are nilpotent.