Probability and a Dirichlet problem for multiply superharmonic functions

Walsh, John B.

Annales de l'Institut Fourier, Tome 18 (1968), p. 221-279 / Harvested from Numdam

Résumé

Soit ${\cal H}$ un préfaisceau complet de fonctions “harmoniques” définies sur $W$. Un critère de régularité pour les points des frontières idéales de $W$ est donné. Pour chaque sous-treillis banachique ${\frak H}$ de ${\cal BH}_W$, il existe une frontière idéale qui compactifie $W$ et qui contient une “frontière harmonique” $\Gamma _{\frak H}$ qui est l’ensemble des points réguliers ; ${\frak H}$ est isométriquement isomorphe à ${\cal C}(\Gamma _{\frak H})$ Parmi des applications se trouvent les théories frontières de Wiener et Royden et aussi les classes comparables harmoniques.

Détail

Publié le : 1968-01-01

Zbl 0172.38702 | 2 citations dans Numdam

DOI : https://doi.org/10.5802/aif.299

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