@Article{JavierGonzálezVieli2013,
author = "Javier González Vieli, Francisco",
title = "A note on bounded harmonic functions over homogeneous trees",
journal = "Opuscula Math.",
year = "2013",
volume = "33",
number = "4",
pages = "697--700",
doi = "http://dx.doi.org/10.7494/OpMath.2013.33.4.697",
url = "http://dx.doi.org/10.7494/OpMath.2013.33.4.697",
abstract = "Let \(\mathcal{T}_k\) be the homogeneous tree of degree \(k\geq 3\). J.M. Cohen and F. Colonna have proved that if \(f\) is a bounded harmonic function on \(\mathcal{T}_k\), then \(|f(x)-f(y)|\leq \|f\|_\infty\cdot 2(k-2)/k\) for any adjacent vertices \(x\) and \(y\) in \(\mathcal{T}_k\). We give here a new and very simple proof of this inequality.",
keywords = "bounded harmonic function, homogeneous tree",
issn = "1232-9274"
}