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Abstract: Let $p$ be a real number greater than one and let $G$ be a finitelygenerated, infinite group. In this paper we introduce the $p$-harmonic boundaryof $G$. We then characterize the vanishing of the first reduced$\ell^p$-cohomology of $G$ in terms of the cardinality of this boundary. Someproperties of $p$-harmonic boundaries that are preserved under rough isometriesare also given. We also study the relationship between translation invariantlinear functionals on a certain difference space of functions on $G$, the$p$-harmonic boundary of $G$ and the first reduced $\ell^p$-cohomology of $G$.



Author: Michael Puls

Source: https://arxiv.org/







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