SEPARATELY ANALYTIC FUNCTIONS, GENERALIZATIONS OF HARTOGS' THEOREM, AND ENVELOPES OF HOLOMORPHY

Let and be arbitrary Stein manifolds, and compact sets, and . Under certain general hypotheses it is proved that a function on which is separately analytic, i.e. for which is analytic in in for any fixed and analytic in in for any fixed , extends to an analytic function in some open neighborhood of which is the envelope of holomorphy of .The envelope of holomorphy of is studied in those cases in which has no open envelope of holomorphy. Bibliography: 26 titles.

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