Abstract:
In this paper, we study the Martin integral representation for nonharmonic functions in
discrete settings of
infinite homogeneous trees.
Recall that the Martin integral representation for trees is analogs to the mean-value
property in Euclidean spaces.
In the Euclidean case, the mean-value property for nonharmonic functions is provided by
the
Pizzetti (and co-Pizzetti) series.
We extend the co-Pizzetti series to the discrete case.
This provides us with an explicit expression
for the discrete mean-value property for nonharmonic functions in discrete settings of
infinite homogeneous trees.
