On Deny's characterization of the potential kernel for a convolution Feller semi-group
Taylor, John C.
Annales de l'Institut Fourier, Tome 25 (1975), p. 519-537 / Harvested from Numdam
Access to full text
Full (PDF)
Full (DJVU)

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.

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.

@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},
     volume = {25},
     year = {1975},
     pages = {519-537},
     doi = {10.5802/aif.596},
     mrnumber = {53 \#5912},
     zbl = {0292.43018},
     language = {en},
     url = {http://dml.mathdoc.fr/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, Tome 25 (1975) pp. 519-537. doi : 10.5802/aif.596. http://gdmltest.u-ga.fr/item/AIF_1975__25_3-4_519_0/

[1] J. Deny, Noyaux de Convolution de Hunt et Noyaux Associés à une Famille Fondamentale, Ann. Inst. Fourier, 12 (1962), 643-667. | Numdam | MR 25 #3189 | Zbl 0101.08302

[2] P. A. Meyer, Probability and Potentials, Blaisdell Publishing Company, Waltham, Mass., 1966. | MR 34 #5119 | Zbl 0138.10401

[3] J.-C. Taylor, On the existence of sub-Markovian resolvents, Invent. Math., 17 (1972), 85-93. | MR 49 #9961 | Zbl 0229.31014

[4] J.-C. Taylor, Ray Processes on Locally Compact Spaces, Math. Annalen. 208 (1974), 233-248. | MR 51 #4424 | Zbl 0266.31006

[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. | Numdam | Zbl 0265.60010