Monique Hakim

Spectre de A(\̄gW) pour des domaines bornés faiblement pseudoconvexes réguliers

Abstract If Ω is a weakly pseudoconvex domain in a Stein manifold, then the spectrum of the Frechet Algebra A ∞ ( \ gW) is isomorphic to \ gW, A ∞ ( \ gW) denotes the space of holomorphic functions smooth up to the boundary. The spectrum of the uniform algebra A( \ gW) is also isomorphic to -Ω. As a corollary we prove an approximation theorem for plurisubharmonic functions in Ω continuous in -Ω.