Maximal Hypoellipticity for Left-Invariant Differential Operators on Lie\n Groups

2018/11/12 by Tommaso Bruno, Bruno, Tommaso
Mathematics · #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1811.05009

Abstract

Given a differential operator defined in terms of left-invariant vector\nfields on a Lie group, we prove that the local condition defining maximal\nhypoellipticity is equivalent to a global estimate if the operator is left\ninvariant. As a consequence, we characterize the domain of the closure in L^p\nof certain maximal hypoelliptic differential operators on test functions on Lie\ngroups.\n

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