A boundary cross theorem for separately holomorphic functions

• Autorzy: Peter Pflug , Viêt-Anh Nguyên
• Języki publikacji: EN

Abstrakty

EN

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 𝓒² 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 crosses is also given.

Kategorie tematyczne

• 32D10: Envelopes of holomorphy
• 32D15: Continuation of analytic objects

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2004
• Tom: 84
• Numer: 3
• Strony: 237-271

Daty

wydano

2004

Twórcy

autor

Peter Pflug

• Fachbereich Mathematik, Carl von Ossietzky Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany

autor

Viêt-Anh Nguyên

• Fachbereich Mathematik, Carl von Ossietzky Universität Oldenburg, Postfach 2503, D-26111, Oldenburg, Germany

Identyfikatory

DOI

10.4064/ap84-3-6