On the solvability of the invariant differential operators on the heisenberg group

Abstract EN

L.Ehrenperis[2] was the first to prove that PD¢ (Rm)=D¢ (Rm) for any invariant differential operator P on R.

The main result is to pove that PD¢ (Hn) = D¢ (Hn) for any invariant differential operator on the real heisebberg group Hn.

Hence to prove the existance of their fundamental soluations, by a transformation, which is associated with the semi-direct product of groups, we construct our method for the division of the distribuations on Hn.

This idea consists of transforming our problem of noncommutative harmonic analysis to an equivalent problem of commutative harmonic analysis.