Journal of Lie Theory Vol. 12, No. 1, pp. 245257 (2002) 

An Invariant Symmetric Nonselfadjoint Differential OperatorErik G. F. ThomasErik G. F. ThomasUniversiteit Groningen Mathematisch Instituut Postbus 800, 9700 AV The Netherlands E.G.F.Thomas@math.rug.nl Abstract: Let $D$ be a symmetric left invariant differential operator on a unimodular Lie group $G$ of type $I$. Then we show that $D$ is essentially selfadjoint if and only if for almost all $\pi \in \widehat{G}$, with respect to the Plancherel measure, the operator $\pi(D)$ is essentially selfadjoint. This, in particular, allows one to exhibit a left invariant symmetric differential operator on the Heisenberg group, which is not essentially selfadjoint. Full text of the article:
Electronic fulltext finalized on: 30 Oct 2001. This page was last modified: 9 Nov 2001.
© 2001 Heldermann Verlag
