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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Keywords: Harmonic function, Martin boundary, random walk, nilpotent group
Mot clés : Fonction harmonique, marche aléatoire, frontière de Martin, groupe nilpotent
Yves Benoist 1
CC-BY 4.0
@article{JEP_2021__8__973_0,
author = {Yves Benoist},
title = {Positive harmonic functions on {the~Heisenberg} group {II}},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {973--1003},
publisher = {\'Ecole polytechnique},
volume = {8},
year = {2021},
doi = {10.5802/jep.163},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.163/}
}
TY - JOUR AU - Yves Benoist TI - Positive harmonic functions on the Heisenberg group II JO - Journal de l’École polytechnique — Mathématiques PY - 2021 SP - 973 EP - 1003 VL - 8 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.163/ DO - 10.5802/jep.163 LA - en ID - JEP_2021__8__973_0 ER -
%0 Journal Article %A Yves Benoist %T Positive harmonic functions on the Heisenberg group II %J Journal de l’École polytechnique — Mathématiques %D 2021 %P 973-1003 %V 8 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.163/ %R 10.5802/jep.163 %G en %F JEP_2021__8__973_0
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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