Texas A&M University, Department of
Mathematics, 216 Milner Hall, 10th of November 2004, 3:00-3:50
Groups and Dynamics Seminar
Asymtpotic behavior
of convolution powers on semisimple groups
Filippo Tolli of
Universitá di Roma Tre, Italy
Let h_t be the heat kernel associated to some left invariant
sublaplacian on a connected Lie group. In the 90's N. Th. Varopoulos
proved that the heat kernel at the identity h_t(e) is comparable, for
t>1, either to exp(-tg-cn^(1/3)) or to t^(-v)exp(-tg), where g is
the spectral gap. The different behavior is explained in terms of the
geometry of the Lie Algebra and it leads to a classification of the Lie
groups into two classes: B and NB. In the setting of semisimple Lie
groups (which are NB groups) Bougerol proved more precise results for
the convolution powers of a measure, using different techniques. We
will show how to extend Bougerol's results to other classes of groups
and to different kind of estimates.