Examples of globally hypoelliptic operator on special dimensional spheres without infinitesimal transitivity
Shimoda, Taishi
Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, p. 112-115 / Harvested from Project Euclid
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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.
Publié le : 2002-09-14
Classification:  Global hypoellipticity,  Omori-Kobayashi conjecture,  35H10,  58J99 
@article{1148392631,
     author = {Shimoda, Taishi},
     title = {Examples of globally hypoelliptic operator on special dimensional spheres without infinitesimal transitivity},
     journal = {Proc. Japan Acad. Ser. A Math. Sci.},
     volume = {78},
     number = {10},
     year = {2002},
     pages = { 112-115},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1148392631}
}

Shimoda, Taishi. Examples of globally hypoelliptic operator on special dimensional spheres without infinitesimal transitivity. Proc. Japan Acad. Ser. A Math. Sci., Tome 78 (2002) no. 10, pp.  112-115. http://gdmltest.u-ga.fr/item/1148392631/