Some results concerning the \(p\)-Royden and \(p\)-harmonic boundaries of a graph of bounded degree (Q2908732)
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scientific article; zbMATH DE number 6077166
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some results concerning the \(p\)-Royden and \(p\)-harmonic boundaries of a graph of bounded degree |
scientific article; zbMATH DE number 6077166 |
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5 September 2012
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infinite graph
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Cayley graph
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finitely generated group
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\(p\)-Royden boundary
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\(p\)-harmonic boundary
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\(p\)-harmonic function
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\(F_{\sigma}\)-set
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0.95141155
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0.9283607
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0.8788253
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0.8693555
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0.8620589
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0.8605033
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Some results concerning the \(p\)-Royden and \(p\)-harmonic boundaries of a graph of bounded degree (English)
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Let \(p >1\) and \(\Gamma\) a connected infinite graph of bounded degree. The main result of this paper is that the \(p\)-Royden boundary of \(\Gamma\) minus the \(p\)-harmonic boundary is a countable union of closed sets. The typical example of \(\Gamma\) is the Cayley graph of a finitely generated group.
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