Ann Mat Pura Appl 2021 29;200(1):35-50. Epub 2020 Apr 29.
Institut für Diskrete Mathematik, Technische Universität Graz, Steyrergasse 30, 8010 Graz, Austria.
This paper studies the boundary behaviour of -polyharmonic functions for the simple random walk operator on a regular tree, where is complex and , the -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. Read More