Rate of decay of concentration functions for spread out measures

Christophe Cuny, Todd Matthew 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
StatePublished - Dec 1 2004

Fingerprint

Concentration Function
Probability Measure
Decay
Discrete Group
Locally Compact
Growth Conditions
Strictly
Subgroup

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

@article{f4fc3cd8f4994949b7c21e4a4ee982d1,
title = "Rate of decay of concentration functions for spread out measures",
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.",
author = "Christophe Cuny and Retzlaff, {Todd Matthew}",
year = "2004",
month = "12",
day = "1",
language = "English (US)",
volume = "48",
pages = "1207--1222",
journal = "Illinois Journal of Mathematics",
issn = "0019-2082",
publisher = "University of Illinois at Urbana-Champaign",
number = "4",

}

Rate of decay of concentration functions for spread out measures. / Cuny, Christophe; Retzlaff, Todd Matthew.

In: Illinois Journal of Mathematics, Vol. 48, No. 4, 01.12.2004, p. 1207-1222.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Rate of decay of concentration functions for spread out measures

AU - Cuny, Christophe

AU - Retzlaff, Todd Matthew

PY - 2004/12/1

Y1 - 2004/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=17244378058&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=17244378058&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:17244378058

VL - 48

SP - 1207

EP - 1222

JO - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

SN - 0019-2082

IS - 4

ER -