An extension theorem for separately holomorphic functions with pluripolar singularities |
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Authors: | Marek Jarnicki Peter Pflug |
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Affiliation: | Jagiellonian University, Institute of Mathematics, Reymonta 4, 30-059 Kraków, Poland ; Carl von Ossietzky Universität Oldenburg, Fachbereich Mathematik, Postfach 2503, D-26111 Oldenburg, Germany |
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Abstract: | Let be a pseudoconvex domain and let be a locally pluriregular set, . Put Let be an open neighborhood of and let be a relatively closed subset of . For let be the set of all for which the fiber is not pluripolar. Assume that are pluripolar. Put Then there exists a relatively closed pluripolar subset of the ``envelope of holomorphy' of such that: , for every function separately holomorphic on there exists exactly one function holomorphic on with on , and is singular with respect to the family of all functions . |
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Keywords: | |
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