Hemigroups of probability measures on a locally compact group
type: Item
instance of: scholarly article
title: Hemigroups of probability measures on a locally compact group
zbMATH Open document ID: 0686.60008
DOI: 10.1007/BF01446921
author: Eike Born
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164713
review text: The author considers hemigroups of probability measures on a locally compact group G, i.e. families \((\mu (s,t))_{0\leq s\leq t}\) of probability measures with \[ \mu (r,s)*\mu (s,t)=\mu (r,t)\quad for\quad 0\leq r\leq s\leq t. \] The corresponding probability operators constitute evolution families on the space \(C_ 0(G)\) of continuous real valued functions on G, vanishing at infinity. He discusses the characterization and generation of hemigroups resp. their evolution families by families of linear operators on \(C_ 0(G)\), which indeed are generators of continuous convolution semigroups of probability measures on G. Two different approaches are presented. The first approach is based on ideas of T. Kato and leads to a self contained presentation of the generation of hemigroups. For the other approach he applies a Hille- Yosida theory for evolutions developed by \textit{J. V. Herod} and \textit{R. W. McKelvey} [Isr. J. Math. 36, 13-40 (1980; Zbl 0452.47044)]. This supplies with a bijective mapping between generator families and hemigroups of bounded variation.
Mathematics Subject Classification ID: 60B15
zbMATH DE Number: 4124685
zbMATH Keywords: hemigroups of probability measures
zbMATH Keywords: characterization and generation of hemigroups
zbMATH Keywords: Hille-Yosida theory
zbMATH Keywords: hemigroups of bounded variation
MaRDI profile type: Publication
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OpenAlex ID: W2066200547
description: scientific article; zbMATH DE number 4124685