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Sept. 2002 Examples of globally hypoelliptic operator on special dimensional spheres without infinitesimal transitivity
Taishi Shimoda
Proc. Japan Acad. Ser. A Math. Sci. 78(7): 112-115 (Sept. 2002). DOI: 10.3792/pjaa.78.112

Abstract

This paper gives examples of globally hypoelliptic operator on $S^3$, or on $S^7$, or on $S^{15}$ which is sum of squares of real vector fields. These operators fail to satisfy the infinitesimal transitivity condition (the Hörmander bracket condition) at every point and therefore they are not hypoelliptic in any subdomain.

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Taishi Shimoda. "Examples of globally hypoelliptic operator on special dimensional spheres without infinitesimal transitivity." Proc. Japan Acad. Ser. A Math. Sci. 78 (7) 112 - 115, Sept. 2002. https://doi.org/10.3792/pjaa.78.112

Information

Published: Sept. 2002
First available in Project Euclid: 23 May 2006

zbMATH: 1034.35015
MathSciNet: MR1930213
Digital Object Identifier: 10.3792/pjaa.78.112

Subjects:
Primary: 35H10
Secondary: 58J99

Keywords: global hypoellipticity , Omori-Kobayashi conjecture

Rights: Copyright © 2002 The Japan Academy

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Vol.78 • No. 7 • Sept. 2002
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