Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-11T10:29:51.387Z Has data issue: false hasContentIssue false
  • English
  • Français

A LIOUVILLE THEOREM FOR MATRIX-VALUED HARMONIC FUNCTIONS ON NILPOTENT GROUPS

Published online by Cambridge University Press:  14 August 2003

CHO-HO CHU  and
TUAN GIAO VU
CHO-HO CHU
Affiliation:
School of Mathematical Sciences, Queen Mary, University of London, London E1 4NS c.chu@qmul.ac.uk
TUAN GIAO VU
Affiliation:
Goldsmiths College, University of London, London SE14 6NW map01tgv@gold.ac.uk
Get access

Abstract

Let $\sigma$ be a non-degenerate positive $M_n$-valued measure on a locally compact group $G$ with $\|\sigma\|\,{=}\,1$. An $M_n$-valued Borel function $f$ on $G$ is called $\sigma$-harmonic if $f(x) = \int_G f(xy^{-1})\,d\sigma(y)$ for all $x\,{\in}\,G$. Given such a function $f$ which is bounded and left uniformly continuous on $G$, it is shown that every central element in $G$ is a period of $f$. Further, it is shown that $f$ is constant if $G$ is nilpotent or central.

Keywords

31C0543A0545E1046G10
Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 35 , Issue 5 , September 2003 , pp. 651 - 658
Copyright
© The London Mathematical Society 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)