-closed extension of CR-forms with singularities on a generic manifold.
Let D ⊂ ℂⁿ and be pseudoconvex domains, let A (resp. B) be an open subset of the boundary ∂D (resp. ∂G) and let X be the 2-fold cross ((D∪A)×B)∪(A×(B∪G)). Suppose in addition that the domain D (resp. G) is locally ² smooth on A (resp. B). We shall determine the “envelope of holomorphy” X̂ of X in the sense that any function continuous on X and separately holomorphic on (A×G)∪(D×B) extends to a function continuous on X̂ and holomorphic on the interior of X̂. A generalization of this result to N-fold...
Using recent development in Poletsky theory of discs, we prove the following result: Let be two complex manifolds, let be a complex analytic space which possesses the Hartogs extension property, let (resp. ) be a non locally pluripolar subset of (resp. ). We show that every separately holomorphic mapping extends to a holomorphic mapping on such that ...
The aim of this paper is to present an extension theorem for (N,k)-crosses with pluripolar singularities.
We characterize composition operators on spaces of real analytic functions which are open onto their images. We give an example of a semiproper map φ such that the associated composition operator is not open onto its image.
Let X be a closed analytic subset of an open subset Omega of Rn. We look at the problem of extending functions from X to Omega.