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arXiv · 1904.10290

Boundary behaviour of $\lambda$-polyharmonic functions on regular trees

Ecaterina Sava-Huss·Wolfgang Woess
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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 $\ell^2$-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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Ecaterina Sava-Huss, Wolfgang Woess. 2019-04-23. Boundary behaviour of $\lambda$-polyharmonic functions on regular trees. https://doi.org/10.1007/s10231-020-00981-8

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