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

 

On certain partial differential operators of finite odd type


Author: A. Alexandrou Himonas
Journal: Trans. Amer. Math. Soc. 324 (1991), 889-900
MSC: Primary 35H05; Secondary 35A27
MathSciNet review: 1055570
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Abstract: Let $ P$ be a linear partial differential operator of order $ m \geqslant 1$ with real-analytic coefficients defined in $ \Omega $, an open set of $ {\mathbb{R}^n}$, and let $ \gamma $ be in the cotangent space of $ \Omega $ minus the zero section. If $ P$ is of odd finite type $ k$ and if the Hörmander numbers are $ 1 = {k_1} < {k_2},{k_2}$ odd, then $ P$ is analytic hypoelliptic at $ \gamma $. These operators are not semirigid.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1991-1055570-9
PII: S 0002-9947(1991)1055570-9
Article copyright: © Copyright 1991 American Mathematical Society