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


Authors: N. Braun Rodrigues, G. Chinni, P. D. Cordaro and M. R. Jahnke
Journal: Proc. Amer. Math. Soc. 144 (2016), 5159-5170
MSC (2010): Primary 35H10, 35H05, 35N15
DOI: https://doi.org/10.1090/proc/13178
Published electronically: May 31, 2016
MathSciNet review: 3556261
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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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Additional Information

N. Braun Rodrigues
Affiliation: Universidade de São Paulo, IME-USP, São Paulo, SP, Brazil
Email: braun@ime.usp.br

G. Chinni
Affiliation: Universidade de São Paulo, IME-USP, São Paulo, SP, Brazil
Email: gregorio.chinni@gmail.com

P. D. Cordaro
Affiliation: Universidade de São Paulo, IME-USP, São Paulo, SP, Brazil
Email: cordaro@ime.usp.br

M. R. Jahnke
Affiliation: Universidade de São Paulo, IME-USP, São Paulo, SP, Brazil
Email: jahnke@ime.usp.br

DOI: https://doi.org/10.1090/proc/13178
Keywords: Sums of squares, global analytic hypoellipticity, Gevrey vectors.
Received by editor(s): October 30, 2015
Received by editor(s) in revised form: January 29, 2016
Published electronically: May 31, 2016
Additional Notes: The first and fourth authors were supported by doctoral fellowships from CNPq
The second author was supported by a posdoctoral fellowship from Fapesp
The third author was partially supported by CNPq and Fapesp
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2016 American Mathematical Society