Lower order perturbation and global analytic vectors for a class of globally analytic hypoelliptic operators (Q2827366)

The authors reconsider the subclass of the Hörmander sum-of-squares operators NEWLINE\[NEWLINEP=- \sum^n_{j=1} L^2_j+ L_0NEWLINE\]NEWLINE on the \(N\)-dimensional torus \(T^N\) introduced by \textit{P. D. Cordaro} and \textit{A. A. Himonas} [Trans. Am. Math. Soc. 350, No. 12, 4993--5001 (1998; Zbl 0914.35087)] who proved global analytic hypoellipticity for \(P+a\) for any analytic function \(a\) on \(T^N\), under suitable assumptions on the structure of the real vector fields \(L_j\), \(j=0,1,\dots,n\).NEWLINENEWLINE As a generalization, in the present paper, the authors prove that analytic hypoellipticity remains valid for lower-order perturbations \(P+A\), provided the order of the analytic pseudo-differential operator \(A\) is smaller than the sub-ellipticity index of \(P\). In the final section of the paper, a different generalization is presented, by replacng \(T^N\) with the product of a compact Lie group and a compact manifold.