Positive harmonic functions on the Heisenberg group II
Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 973-1003.

We describe the extremal positive harmonic functions for finitely supported measures on the discrete Heisenberg group: they are proportional either to characters or to translates of induced from characters.

Nous décrivons les fonctions harmoniques positives extrémales pour les mesures à support fini sur le groupe de Heisenberg discret : elles sont proportionnelles à des caractères ou à des translatées d’induites de caractères.

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DOI: 10.5802/jep.163
Classification: 31C35,  60B15,  60G50,  60J50
Keywords: Harmonic function, Martin boundary, random walk, nilpotent group
Yves Benoist 1

1 IMO, CNRS, Université Paris-Saclay Bâtiment 307, 91405 Orsay, France
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Yves Benoist. Positive harmonic functions on the Heisenberg group II. Journal de l’École polytechnique — Mathématiques, Volume 8 (2021), pp. 973-1003. doi : 10.5802/jep.163. https://jep.centre-mersenne.org/articles/10.5802/jep.163/

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