The Rate of Decay of Concentration Functions on Locally Compact Groups
Retzlaff, Todd M.
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https://hdl.handle.net/2142/87006
Description
Title
The Rate of Decay of Concentration Functions on Locally Compact Groups
Author(s)
Retzlaff, Todd M.
Issue Date
2000
Doctoral Committee Chair(s)
Joseph Max Rosenblatt
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
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.
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