Harmonic functions along Brownian balls and the Liouville property for solvable Lie groups
type: Item
instance of: scholarly article
title: Harmonic functions along Brownian balls and the Liouville property for solvable Lie groups
zbMATH Open document ID: 0806.60061
DOI: 10.1007/BF01445121
author: Bernhard Leeb
published in: Mathematische Annalen
publication date: 1994-04-26T00:00:00Z
full work available at URL: https://eudml.org/doc/165101
review text: Let \(G\) be a connected Lie group, \(g\) be its Lie algebra, \(E_ i\) be an orthonormal basis of \(g\), \((W_ t)\) be the standard Brownian motion on \(R^{\dim G}\). \((X_ t)\) is called canonical diffusion on \(G\) if \(dX_ t = \sum_ i E_ i (X_ t) \circ dW^ i_ t\). Recall that the Liouville property states that every bounded harmonic function is constant. Theorem 2. The canonical diffusion on a connected solvable Lie group \(G\) is Liouville.
Mathematics Subject Classification ID: 60J60
Mathematics Subject Classification ID: 60B15
Mathematics Subject Classification ID: 60J65
zbMATH DE Number: 537269
zbMATH Keywords: diffusion processes
zbMATH Keywords: Lie group
zbMATH Keywords: Liouville property
zbMATH Keywords: harmonic function
zbMATH Keywords: solvable Lie group
MaRDI profile type: Publication
Wikidata QID: Q115393529
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description: scientific article; zbMATH DE number 537269