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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Remarks about global analytic hypoellipticity


Author: Adalberto P. Bergamasco
Journal: Trans. Amer. Math. Soc. 351 (1999), 4113-4126
MSC (1991): Primary 35H05
Published electronically: March 19, 1999
MathSciNet review: 1603878
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Abstract: We present a characterization of the operators

\begin{displaymath}L=\partial/\partial t+(a(t)+ib(t))\partial/\partial x\end{displaymath}

which are globally analytic hypoelliptic on the torus. We give information about the global analytic hypoellipticity of certain overdetermined systems and of sums of squares.


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Additional Information

Adalberto P. Bergamasco
Email: apbergam@power.ufscar.br

DOI: http://dx.doi.org/10.1090/S0002-9947-99-02299-0
PII: S 0002-9947(99)02299-0
Keywords: Global analytic hypoellipticity, exponential Liouville numbers, exponential Liouville vectors, steepest descent, involutive systems, continued fractions.
Received by editor(s): July 19, 1996
Received by editor(s) in revised form: September 29, 1997
Published electronically: March 19, 1999
Additional Notes: The author was partially supported by CNPq.
Dedicated: Dedicated to Antonio Gilioli, in memoriam
Article copyright: © Copyright 1999 American Mathematical Society