Hokkaido Mathematical Journal

SHIMODA Taishi,

Examples of globally hypoelliptic operator on special dimensional spheres without the bracket condition.

Hokkaido Mathematical Journal, 34 (2005) pp.219-235

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Abstract

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

MSC(Primary)35H10
MSC(Secondary)58J99
Uncontrolled Keywordsglobal hypoellipticity, Omori-Kobayashi conjecture