  In 1980, J. Roe proved that if $\{f_{k}\}_{k\in\mathbb{Z}}$ is doubly
infinite sequence of functions in $\mathbb{R}$ which is uniformly bounded and
satisfies $(df_{k}/dx)=f_{k+1}$ for all $k\in\mathbb{Z}$ then
$f_{0}(x)=a\sin(x+\theta)$ for some $a,\theta\in\mathbb{R}$. Later in 1993
Strichartz suitably extended the above result to $\mathbb{R}^n$. In this
article we prove a version of their result for homogeneous trees.
