Geodesic
Maximal Hypoellipticity for Left-Invariant Differential Operators on Lie Groups
Journal of Lie theory, Tome 29 (2019) no. 3, pp. 801-809
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Given a maximal hypoelliptic differential operator of arbitrary order, we prove that its graph norm controls the Sobolev norm of the same order if the operator has left-invariant principal part and lower order terms with bounded coefficients. As an application, we obtain the essential self-adjointness on L2 of Rumin's Laplacians on the contact complex of the Heisenberg groups.
Classification : 35H10, 35H20, 22E30
Mots-clés : Maximal hypoellipticity, Lie groups, Laplace operators 
@article{JLT_2019_29_3_JLT_2019_29_3_a8,
     author = {T. Bruno},
     title = {Maximal {Hypoellipticity} for {Left-Invariant} {Differential} {Operators} on {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {801--809},
     year = {2019},
     volume = {29},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2019_29_3_JLT_2019_29_3_a8/}
}
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T. Bruno. Maximal Hypoellipticity for Left-Invariant Differential Operators on Lie Groups. Journal of Lie theory, Tome 29 (2019) no. 3, pp. 801-809. http://geodesic.mathdoc.fr/item/JLT_2019_29_3_JLT_2019_29_3_a8/