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Il est démontré que l’espace des fonctions holomorphes sur un sous-espace homogène , au sens de Katznelson, de muni de la topologie engendrée par les semi-normes portées par les compacts de , est bornologique.
Les propriétés générales des fonctions plurisousharmoniques définies sur une partie -ouverte d’un e.v.t. sont établies. Lorsque est supposé quasi-complet, l’auteur généralise la mesure de Cauchy aux “polycercles”. À l’aide de ces mesures, l’auteur étend à la dimension infinie quelques propriétés des ensembles strictement polaires.
Dans une seconde partie, la caractérisation de Bremermann des ensembles pseudo-convexes est étendue à une variété , étalée sur un espace de Banach ....
On démontre que les domaines bornés, pseudo-convexes, à frontière lisse, de type fini dans , ayant un groupe d’automorphismes non compact sont biholomorphes à des domaines de la forme , où est un polynôme sousharmonique dont le degré est majoré par le type de la frontière du domaine.
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