On the Existence Theorem For Invariant Differential Operators on The Heisenberg group

F. Treves in hisn book, Linear Partial Differential Equations with Constant Coefficients has proved that for any invariant differential operator P on ℝ^m [6]. The main object of this paper is to generalize this result for any invariant differential operator on Hⁿ the Heisenberg group of dimension 2n+1, so that we get the existence theorem for these operatrs. Our appraoch is to transform the problem in the non commutative harmonic analysis to an equivalent problem in commutative harmonic analysis. Since the Lewy operator is among of these operators (see A. Cerezo and F. Rouviere, Résolubilité Local d'um Opérateur Différéntiel Invariant Du Premier Order), I believe that this note will be intended to draw the attention of analyst to this way in the theory of differential equations with variables coefficients.