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Boundary behaviour of $λ$-polyharmonic functions on regular trees (1904.10290v2)
Published 23 Apr 2019 in math.PR
Abstract: This paper studies the boundary behaviour of $\lambda$-polyharmonic functions for the simple random walk operator on a regular tree, where $\lambda$ is complex and $|\lambda|> \rho$, the $\ell2$-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.