The Rate of Decay of Concentration Functions on Locally Compact Groups

Given an adapted probability measure on a locally compact group, there are a variety of support conditions which cause the concentration functions to go to zero. This work discusses the rate of this decay under many such conditions. This work focuses primarily on concentration functions for discrete groups, though some results are also obtained for non-discrete groups. In particular, we show that, when G is discrete and satisfies the volume growth condition V(n) ≥ cnD , then if the concentration functions go to zero they do so at a rate of at least O(k-D /2). These results are based heavily on the work of Varopoulos, Saloff-Coste, and Colhoun.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Retzlaff, Todd M.

Contributors dc:contributor

• Joseph Max Rosenblatt

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9990125

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/87006