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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Global analytic and Gevrey hypoellipticity of sublaplacians under Diophantine conditions


Author: A. Alexandrou Himonas
Journal: Proc. Amer. Math. Soc. 129 (2001), 2061-2067
MSC (1991): Primary 35H05
Published electronically: December 4, 2000
MathSciNet review: 1825918
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Abstract:

In this paper we consider the problem of global Gevrey and analytic regularity for a class of partial differential operators on a torus in the form of a sum of squares of vector fields, which may not satisfy the bracket condition. We show that these operators are globally Gevrey or analytic hypoelliptic on the torus if and only if the coefficients satisfy certain Diophantine approximation properties.


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Additional Information

A. Alexandrou Himonas
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: himonas.1@nd.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05996-7
PII: S 0002-9939(00)05996-7
Keywords: Global, analytic and Gevrey hypoellipticity, Diophantine conditions, torus, Fourier transform, bracket condition
Received by editor(s): November 15, 1999
Published electronically: December 4, 2000
Additional Notes: The author was supported in part by NSF Grant DMS-9970857.
Communicated by: David S. Tartakoff
Article copyright: © Copyright 2000 American Mathematical Society