Dans cet article on montre que toute a une décomposition avec pour les domaines pseudoconvexes à frontière réelle-analytique et aussi pour les domaines pseudoconvexes pour lesquels le résultat soit valable localement.
In this paper we give characterizations of those holomorphic functions in the unit disc in the complex plane that can be written as a quotient of functions in A(D), A(D) or Λ(D) with a nonvanishing denominator in D. As a consequence we prove that if f ∈ Λ(D) does not vanish in D, then there exists g ∈ Λ(D) which has the same zero set as f in Dbar and such that fg ∈ A(D).
Let D be a bounded strictly pseudoconvex domain of Cn with C ∞ boundary and Y = {z; u1(z) = ... = ul(z) = 0} a holomorphic submanifold in the neighbourhood of D', of codimension l and transversal to the boundary of D. In this work we give a decomposition formula f = u1f1 + ... + ulfl for functions f of the Bergman-Sobolev space...
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