An extension theorem for separately holomorphic functions with analytic singularities
Marek Jarnicki, Peter Pflug (2003)
Annales Polonici Mathematici
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Let be a pseudoconvex domain and let be a locally pluriregular set, j = 1,...,N. Put . 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 . The result generalizes special cases which were studied in [Ökt 1998], [Ökt 1999], [Sic 2001], and [Jar-Pfl 2001]. ...