Positive harmonic functions on the Heisenberg group. II (Q2028052)
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| English | Positive harmonic functions on the Heisenberg group. II |
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Positive harmonic functions on the Heisenberg group. II (English)
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Positive harmonic functions on the Heisenberg group. I (English)
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31 May 2021
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10 November 2023
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This article discusses extremal positive harmonic functions for finitely supported measures on the discrete Heisenberg group. The author establishes that extremal positive harmonic functions are proportional either to characters or to translates of induced from characters. For Part I, see [the author, ``Positive Harmonic Functions on the Heisenberg group. I'', Preprint, \url{arXiv:1907.05041}].
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In the paper under review, the author presents the classification of the positive harmonic functions on the Heisenberg group \(H_3(\mathbb{Z})\) in the special case of the southwest measure. Then the author explains how the result can be extended to finite positive measures on \(H_3(\mathbb{Z})\). For the entire collection see [Zbl 1519.00033].
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harmonic function
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Martin boundary
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random walk
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nilpotent group
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harmonic functions on the Heisenberg group
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southwest measure
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nilpotent groups
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0.98461473
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0.93126744
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0.92030805
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0.9138075
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0.9115056
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0.8981811
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0.89770734
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0.8968151
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