On Deny's characterization of the potential kernel for a convolution Feller semi-group
Annales de l'Institut Fourier, Volume 25 (1975) no. 3-4, p. 519-537

The convolution kernels $Vf=f*x$ on a homogeneous space $E=G/K$, where $K$ is a compact sub-group of $G$, that satisfy the complete maximum principle are characterized.

Deny’s result for abelian groups $G$, but with a stronger hypothesis, is a special case.

On caractérise les noyaux $Vf=f*k$ de convolution sur un espace homogène $E=G/K$$K$ est un sous-groupe compact de $G$, qui satisfont au principe complet du maximum. Comme cas particulier on obtient le résultat de Deny, mais sous une hypothèse plus forte, pour les groupes $G$ abéliens.

@article{AIF_1975__25_3-4_519_0,
author = {Taylor, John C.},
title = {On Deny's characterization of the potential kernel for a convolution Feller semi-group},
journal = {Annales de l'Institut Fourier},
publisher = {Imprimerie Durand},
volume = {25},
number = {3-4},
year = {1975},
pages = {519-537},
doi = {10.5802/aif.596},
zbl = {0292.43018},
mrnumber = {53 \#5912},
language = {en},
url = {http://www.numdam.org/item/AIF_1975__25_3-4_519_0}
}

Taylor, John C. On Deny's characterization of the potential kernel for a convolution Feller semi-group. Annales de l'Institut Fourier, Volume 25 (1975) no. 3-4, pp. 519-537. doi : 10.5802/aif.596. http://www.numdam.org/item/AIF_1975__25_3-4_519_0/

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