Positive harmonic functions on the Heisenberg group II
[Fonctions harmoniques positives sur le groupe de Heisenberg II]
Benoist, Yves1
1 IMO, CNRS, Université Paris-Saclay Bâtiment 307, 91405 Orsay, France
Journal de l’École polytechnique — Mathématiques, Tome 8 (2021), pp. 973-1003.

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.

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.

Reçu le :
Accepté le :
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DOI : 10.5802/jep.163
Classification : 31C35, 60B15, 60G50, 60J50
Keywords: Harmonic function, Martin boundary, random walk, nilpotent group
Mot clés : Fonction harmonique, marche aléatoire, frontière de Martin, groupe nilpotent
Benoist, Yves 1

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

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