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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].
$X: = ⋃_{j=1}^N A₁ ×. .. × A_{j-1} × D_j × A_{j+1} ×. .. × A_N ⊂ ℂ^{k₁+...+k_N}$.
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].
Słowa kluczowe
Kategorie tematyczne
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Rocznik
Tom
Numer
Strony
143-161
Opis fizyczny
Daty
wydano
2003
Twórcy
autor
- Institute of Mathematics, Jagiellonian University, Reymonta 4, 30-059 Kraków, Poland
autor
- Fachbereich Mathematik, Carl von Ossietzky Universität Oldenburg, Postfach 2503, D-26111 Oldenburg, Germany
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bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-12