This paper studies the boundary behaviour of λ-polyharmonic functions for the simple random walk operator on a regular tree, where λ is complex and |λ>ρ, the ℓ2-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.
ASJC Scopus subject areas
- Angewandte Mathematik
Fields of Expertise
- Information, Communication & Computing