no. 3-4
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

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 où 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.

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
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[1] J. Deny, Noyaux de Convolution de Hunt et Noyaux Associés à une Famille Fondamentale, Ann. Inst. Fourier, 12 (1962), 643-667. | Zbl | MR | Numdam

[2] P. A. Meyer, Probability and Potentials, Blaisdell Publishing Company, Waltham, Mass., 1966. | Zbl | MR

[3] J.-C. Taylor, On the existence of sub-Markovian resolvents, Invent. Math., 17 (1972), 85-93. | Zbl | MR

[4] J.-C. Taylor, Ray Processes on Locally Compact Spaces, Math. Annalen. 208 (1974), 233-248. | Zbl | MR

[5] J.-C. Taylor, On the existence of resolvents, Séminaire de probabilité VII, Université de Strasbourg (1971-1972), Springer, Lecture Notes, 321, 291-300, Berlin, 1973. | Zbl | Numdam

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