La soluzione fondamentale per i sub-laplaciani sui gruppi nilpotenti di passo due.

The aim of the thesis is to provide a new approach to the proof of Beals, Gaveau, Greiner [Adv. Math.1996] which gives an explicit integral representation of the fundamental solution G of each sub-Laplacian L on Carnot groups of step 2. The main new feature lies in bringing the verification distributional equation LG = Dirac_0 to test some simple properties, necessary and sufficient conditions that a function is the fundamental solution of L. These properties are verified in a natural way by the above integral expression of G. It also gives examples of calculation of some fundamental solutions (necessarily by the use of software).