Boundary behaviour of $λ$-polyharmonic functions on regular trees

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 $\ell^2$-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.

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