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A boundary cross theorem for separately holomorphic functions

Peter Pflug, Viêt-Anh Nguyên (2004)

Annales Polonici Mathematici

Let D ⊂ ℂⁿ and G ⊂ ℂ m 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...

A general version of the Hartogs extension theorem for separately holomorphic mappings between complex analytic spaces

Viêt-Anh Nguyên (2005)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Using recent development in Poletsky theory of discs, we prove the following result: Let X , Y be two complex manifolds, let Z be a complex analytic space which possesses the Hartogs extension property, let A (resp. B ) be a non locally pluripolar subset of X (resp. Y ). We show that every separately holomorphic mapping f : W : = ( A × Y ) ∪ ( X × B ) → Z extends to a holomorphic mapping f ^ on W ^ : = ( z , w ) ∈ X × Y : ω ˜ ( z , A , X ) + ω ˜ ( w , B , Y ) < 1 such that f ^ = f ...

A note on composition operators on spaces of real analytic functions

Paweł Domański, Michał Goliński, Michael Langenbruch (2012)

Annales Polonici Mathematici

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.

A remark on Nilsson type integrals

Nguyen Minh, Bogdan Ziemian (1996)

Banach Center Publications

We investigate ramification properties with respect to parameters of integrals (distributions) of a class of singular functions over an unbounded cycle which may intersect the singularities of the integrand. We generalize the classical result of Nilsson dealing with the case where the cycle is bounded and contained in the set of holomorphy of the integrand. Such problems arise naturally in the study of exponential representation at infinity of solutions to certain PDE's (see [Z]).

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