On left-invariant Hormander operators in R^N: applications to the Kolmogorov-Fokker-Planck equations (Russian Version)

If L is a Hormander partial differential operator in R^N, we give sufficient conditions for the existence of a Lie group structure G = (R^N; ¤), not necessarily nilpotent, such that L is left invariant on G. We also investigate the existence of a global fundamental solution ¡ for L, providing results ensuring a suitable left invariance property of ¡. Examples are given for operators L to which our results apply: some are new, some appear in recent literature, usually quoted as Kolmogorov-Fokker-Planck type operators. Non trivial examples of homogeneous groups are also given.