Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups
type: Item
instance of: scholarly article
title: Automorphisms on a Lie group contracting modulo a compact subgroup and applications to semistable convolution semigroups
zbMATH Open document ID: 0659.60020
DOI: 10.1007/BF01046936
published in: Journal of Theoretical Probability
publication date: 1988-01-01T00:00:00Z
review text: Let \((\mu_ t)_{t\geq 0}\) be a \(\tau\)-semistable convolution semigroup of probability measures on a Lie group G whose idempotent \(\mu_ 0\) is the Haar measure on some compact subgroup K. Then all the measures \(\mu_ t\) are supported by the K-contraction group \(C_ K(\tau)\) of the topological automorphism \(\tau\) of G. We prove here the structure theorem \(C_ K(\tau)=C(\tau)K\), where C(\(\tau)\) is the contraction group of \(\tau\). Then it turns out that it is sufficient to study semistable convolution semigroups on simply connected nilpotent Lie groups that have Lie algebras with a positive graduation.
Mathematics Subject Classification ID: 60B15
zbMATH DE Number: 4078353
zbMATH Keywords: convolution semigroup of probability measures
zbMATH Keywords: topological automorphism
zbMATH Keywords: simply connected nilpotent Lie groups
zbMATH Keywords: Lie algebras
Wikidata QID: Q115394582
author: Wilfried Hazod
author: Eberhard Siebert
MaRDI profile type: Publication
cites work: Continuous automorphism groups on a locally compact group contracting modulo a compact subgroup and applications to stable convolution semigroups
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full work available at URL: https://doi.org/10.1007/bf01046936
OpenAlex ID: W2015726409
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description: scientific article; zbMATH DE number 4078353