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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On certain partial differential operators of finite odd type
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by A. Alexandrou Himonas PDF
Trans. Amer. Math. Soc. 324 (1991), 889-900 Request permission

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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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 324 (1991), 889-900
  • MSC: Primary 35H05; Secondary 35A27
  • DOI: https://doi.org/10.1090/S0002-9947-1991-1055570-9
  • MathSciNet review: 1055570