An extension theorem for separately holomorphic functions with analytic singularities

Marek Jarnicki; Peter Pflug

Annales Polonici Mathematici, Tome 81 (2003), p. 143-161 / Harvested from The Polish Digital Mathematics Library

Résumé

Let $D_{j} \subset ℂ^{k_{j}}$ be a pseudoconvex domain and let $A_{j} \subset D_{j}$ be a locally pluriregular set, j = 1,...,N. Put $X : = ⋃_{j = 1}^{N} A ₁ \times . . . \times A_{j - 1} \times D_{j} \times A_{j + 1} \times . . . \times A_{N} \subset ℂ^{k ₁ + . . . + k_{N}}$ . 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 ${f ̂ |}_{X ∖ M} = f$ . The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001].

Publié le : 2003-01-01

Zbl 1023.32001

EUDML-ID : urn:eudml:doc:281010

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Marek Jarnicki; Peter Pflug. An extension theorem for separately holomorphic functions with analytic singularities. Annales Polonici Mathematici, Tome 81 (2003) pp. 143-161. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap80-0-12/