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- W2012123679 abstract "Soit Eun groupe connexe, localement connexe, localement compact qui possède une base dénombrable de voisinages. Existe-t-il sur E un faisceau invariant de fonctions harmoniques satisfaisant l'axiomatique de Brelot ? Pour quels groupes E les axiomatiques de Bauer et Brelot coïncident-elles pour tous les faisceaux harmoniques elliptiques invariants? Cette note annonce les réponses suivantes à ces questions: (a) Tout groupe E posséde un faisceau harmonique au sens de Brelot. (b) Les seuls groupes sur lesquels les axiomatiques de Bauer et Brelot coïncident pour tout faiceau harmonique elliptique invariant sont les groupes de Lie. Ces résultats sont obtenus par l'étude de diffusions produits sur des produits infinis de variétés, e.g., de groupes de Lie compacts. Let F. be a connected amd locally connected locally compact group having a countable basis for its topology. Does E admit a translation invariant Brelot harmonic sheaf? For which E does the elliptic Bauer theory coincides with the Brelot theory for all invariant harmonic elliptic sheaves? This note announces the following solutions: (a) Any E carries invariant Brelot harmonic sheaves; (b) Any invariant elliptic Bauer harmonic elliptic sheaf is a Brelot sheaf if and only if E is a finite dimensional Lie group. These results are obtained by studying product diffusions on infinite products of manifolds. e.g.. compacts Lie groups." @default.
- W2012123679 created "2016-06-24" @default.
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- W2012123679 date "1997-04-01" @default.
- W2012123679 modified "2023-09-30" @default.
- W2012123679 title "Théorie du potentiel sur les produits infinis et les groupes localement compacts" @default.
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- W2012123679 doi "https://doi.org/10.1016/s0764-4442(97)86943-1" @default.
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