Formula di Taylor nei gruppi di Carnot e applicazioni

In ’82 Folland and Stein defined, for a given function f of class C^n(G), the Taylor polynomial, where G is a connected and simply connected real Lie group whose algebra is endowed with a family of dilations δ_λ. Although the extensive studies in this field, particularly in the case of stratified groups nowadays called Carnot groups, an explicit representation of the nth–Taylor polynomial in this last setting seems to be missing. In this note we announce an explicit expression for the Taylor polynomial when G is the Heisenberg group H^1 , and we present one application.