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- Title
On the hypoellipticity of sub-Laplacians on in .nite dimensional compact groups.
- Authors
Bendikov, Alexandre; Saloff-Coste, Laurent
- Abstract
This paper studies the hypoellipticity of infinitesimal generators of central Gaussian convolution semigroups on compact connected groups. Several notions of hypoellipticity arc introduced and discussed. The strongest of these notions involves Bruhat distributions. We show that this strong hypoelliticity cannot hold unless the group is a finite dimensional Lie group. A weaker notion of hypoellipticity involves Borel measures. We show that this weaker hypoellipticity is meaningful on any compact connected locally connected metrizable group.
- Subjects
HYPOELLIPTIC differential equations; LAPLACIAN operator; SEMIGROUPS (Algebra); GROUP theory; LIE algebras
- Publication
Forum Mathematicum, 2003, Vol 15, Issue 1, p135
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/form.2003.003