Opuscula Math. 33, no. 4 (2013), 697-700
http://dx.doi.org/10.7494/OpMath.2013.33.4.697
Opuscula Mathematica
A note on bounded harmonic functions over homogeneous trees
Francisco Javier González Vieli
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.
Mathematics Subject Classification: 31C20, 05C05, 05C63.
- Francisco Javier González Vieli
- Montoie 45, 1007 Lausanne, Switzerland
- Received: 2013-04-22.
- Accepted: 2013-05-22.
