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# Some remarks concerning harmonic functions on homogeneous graphs

Abstract : We obtain a new result concerning harmonic functions on infinite Cayley graphs $X$: either every nonconstant harmonic function has infinite radial variation in a certain uniform sense, or there is a nontrivial boundary with hyperbolic properties at infinity of $X$. In the latter case, relying on a theorem of Woess, it follows that the Dirichlet problem is solvable with respect to this boundary. Certain relations to group cohomology are also discussed.
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Cited literature [11 references]

https://hal.inria.fr/hal-01183944
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Submitted on : Wednesday, August 12, 2015 - 9:08:41 AM
Last modification on : Thursday, May 11, 2017 - 1:02:54 AM
Long-term archiving on: : Friday, November 13, 2015 - 11:38:19 AM

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### Citation

Anders Karlsson. Some remarks concerning harmonic functions on homogeneous graphs. Discrete Random Walks, DRW'03, 2003, Paris, France. pp.137-144, ⟨10.46298/dmtcs.3348⟩. ⟨hal-01183944⟩

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