An extension theorem for separately holomorphic functions with analytic singularities

• Autorzy: Marek Jarnicki , Peter Pflug
• Języki publikacji: EN

Abstrakty

EN

Let $D_j ⊂ ℂ^{k_j}$ be a pseudoconvex domain and let $A_j ⊂ D_j$ be a locally pluriregular set, j = 1,...,N. Put
$X: = ⋃_{j=1}^N A₁ ×. .. × A_{j-1} × D_j × A_{j+1} ×. .. × A_N ⊂ ℂ^{k₁+...+k_N}$.
Let U be an open connected neighborhood of X and let M ⊊ U be an analytic subset. Then there exists an analytic subset M̂ of the "envelope of holomorphy" X̂ of X with M̂ ∩ X ⊂ M such that for every function f separately holomorphic on X∖M there exists an f̂ holomorphic on X̂∖M̂ with $f̂|_{X∖M} = f$. The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001].

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 2003
• Tom: 80
• Numer: 1
• Strony: 143-161

Daty

wydano

2003

Twórcy

autor

Marek Jarnicki

• Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland

autor

Peter Pflug

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

Identyfikatory

DOI

10.4064/ap80-0-12