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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 $G \subset ℂ^{m}$ 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 correction to and a remark on our paper "Remarks on the proof of a generalized Hartogs Lemma" (Ann. Polon. Math. 70 (1998), 43-47)

Evgeni Chirka, Jean-Pierre Rosay (2004)

Annales Polonici Mathematici

A Formula for Interpolation and Division in Cn.

Bo Berndtsson (1983)

Mathematische Annalen

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 $f : W : = (A \times Y) \cup (X \times B) \to Z$ extends to a holomorphic mapping $\hat{f}$ on $\hat{W} : = \{(z, w) \in X \times Y : \tilde{ω} (z, A, X) + \tilde{ω} (w, B, Y) < 1\}$ such that $\hat{f} = f$ ...

A generalization of the Malgrange-Zerner theorem

Ludwik M. Drużkowski (1980)

Annales Polonici Mathematici

A generalized complex Hopf Lemma and its applications to CR mappings.

Linda Preiss Rothschild, M.S. Bouendi (1993)

Inventiones mathematicae

A Hartogs type extension theorem for generalized (N,k)-crosses with pluripolar singularities

Małgorzata Zajęcka (2012)

Colloquium Mathematicae

The aim of this paper is to present an extension theorem for (N,k)-crosses with pluripolar singularities.

A lemma on mixed derivatives with applications to edge-of-the-wedge, Radon transformation and a theorem of Forelli

J. Wiegerinck, J. Korevaar (1985)

Matematički Vesnik

A new proof of a theorem of Grauert and Remmert by L2-Methods.

Gerd-E. Dethloff (1990)

Mathematische Annalen

A Note Concerning Radó's Theorem.

Juhani Riihentaus (1983)

Mathematische Zeitschrift

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 note on Liouville analytic spaces

Sławomir Cynk (1990)

Annales Polonici Mathematici

A note on pluripolar extensions of univalent functions.

Sičiak, Józef (2006)

Zeszyty Naukowe Uniwersytetu Jagiellońskiego. Universitatis Iagellonicae Acta Mathematica

A note on the extension of analytic functions off real analytic subsets.

G. Nardelli, A. Tancredi (1996)

Revista Matemática de la Universidad Complutense de Madrid

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.

A Precise Result on the Boundary Regularity of Biholomorphic Mappings.

László Lempert (1986)

Mathematische Zeitschrift

A Reflection Principle for Proper Holomorphic Mappings of Strongly Pseudoconvex Domains and Applications.

J.A. Cima, S.G. Krantz, T. Suffridge (1984)

Mathematische Zeitschrift

A reflection principle on strongly pseudoconvex domains with generic corners.

Franc Forstneric (1993)

Mathematische Zeitschrift

A Reflection Principle with Applications to Proper Holomorphic Mappings.

J.A. Cima, T.J. Suffridge (1983)

Mathematische Annalen

A Remark on a Paper by S.R. Bell.

J.E. Fornaess, K. Diederich (1981)

Manuscripta mathematica

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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