Evgueni Klebanov

Ph.D. (2007) Cornell University

Dissertation

Asymptotic Behavior of Convolutions of Centered Density on Lie Group of Polynomial Volume Growth

Advisor

Abstract

The main goal of the thesis is to study the behavior of convolution powers of centered density φ on polynomial volume growth Lie group. We prove |φ∗n(e) – c1n–D/2| ≤ c2 n–(D + γ)/2, where D is a homogeneous dimension of the group and 0 < γ ≤ 1. This is achieved by comparison to appropriate heat kernel, which lives on the same underlying space with possibly different Lie brackets. This extends results due to Alexopoulos who treats compactly supported densities.