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

Braun Rodrigues, N.; Chinni, G.; Cordaro, P.; Jahnke, M.

doi:10.1090/proc/13178

Lower order perturbation and global analytic vectors for a class of globally analytic hypoelliptic operators
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by N. Braun Rodrigues, G. Chinni, P. D. Cordaro and M. R. Jahnke

Proc. Amer. Math. Soc. 144 (2016), 5159-5170

DOI: https://doi.org/10.1090/proc/13178

Published electronically: May 31, 2016

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Abstract:

In this work we return to the class of globally analytic hypoelliptic Hörmander’s operators defined on the $N$-dimensional torus introduced by Cordaro and Himonas and prove that if $P$ is any operator in this class, then a perturbation of $P$ by an analytic pseudodifferential operator with degree smaller than the subelliptic index of $P$ remains globally analytic hypoelliptic. We also study the Gevrey regularity of the Gevrey vectors for such a class and at the end we also show that Cordaro and Himonas’s result can be extended to a similar class of operators now defined in a product of compact Lie group by a compact manifold.

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