Abstract
The main result is Theorem 1. If is a holomorphic function on the polydisk in , and for each fixed in some nonpluripolar set the function can be continued holomorphically to the whole plane with the exception of some polar set of singularities, then can be continued holomorphically to , where is a closed pluripolar subset of . Some generalizations are also given, along with corollaries on extension of functions with analytic sets of singularities. Bibliography: 13 titles.
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