A Theorem of Roe and Strichartz on homogeneous trees

Abstract

In 1980, J. Roe proved that if {f k } k∈Z is doubly infinite sequence of functions in R which is uniformly bounded and satisfies (df k /dx) = f k+1 for all k ∈ Z then f0(x) = a sin(x+θ) for some a, θ ∈ R. Later in 1993 Strichartz suitably extended the above result to R n . In this article we prove a version of their result for homogeneous trees.