Author:
Sava-Huss Ecaterina,Woess Wolfgang
Abstract
AbstractThis paper studies the boundary behaviour of $$\lambda $$
λ
-polyharmonic functions for the simple random walk operator on a regular tree, where $$\lambda $$
λ
is complex and $$|\lambda |> \rho $$
|
λ
|
>
ρ
, the $$\ell ^2$$
ℓ
2
-spectral radius of the random walk. In particular, subject to normalisation by spherical, resp. polyspherical functions, Dirichlet and Riquier problems at infinity are solved, and a non-tangential Fatou theorem is proved.
Publisher
Springer Science and Business Media LLC
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