TY  - JOUR
ID  - JavierGonzálezVieli2013
LB  - JavierGonzálezVieli2013
AU  - Javier González Vieli, Francisco
TI  - A note on bounded harmonic functions over homogeneous trees
ST  - A note on bounded harmonic functions over homogeneous trees
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2013
VL  - 33
IS  - 4
SP  - 697
EP  - 700
DO  - http://dx.doi.org/10.7494/OpMath.2013.33.4.697
UR  - http://dx.doi.org/10.7494/OpMath.2013.33.4.697
AB  - 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.
KW  - bounded harmonic function
KW  - homogeneous tree
SN  - 1232-9274
ER  -