Rate of decay of concentration functions for spread out measures

Christophe Cuny, Todd Retzlaff

Research output: Contribution to journalArticle

Abstract

Let G be a locally compact unimodular group and μ an adapted spread out probability measure on G. We relate the rate of decay of the concentration functions associated with μ. to the growth of a certain subgroup N μ of G. In particular, we show that when μ. is strictly aperiodic (i.e., when Nμ= G) and G satisfies the growth condition VG(m) ≥ CmD, then for any compact neighborhood K ⊂ G we have supg∈G μ*n(gK) ≤ C′n -D/2. This extends recent results of Retzlaff [R2] on discrete groups for adapted probability measures.

Original languageEnglish (US)
Pages (from-to)1207-1222
Number of pages16
JournalIllinois Journal of Mathematics
Volume48
Issue number4
DOIs
StatePublished - Jan 1 2004

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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