About: Malgrange–Zerner theorem

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In mathematics, Malgrange–Zerner theorem (named for Bernard Malgrange and ) shows that a function on allowing holomorphic extension in each variable separately can be extended, under certain conditions, to a function holomorphic in all variables jointly. This theorem can be seen as a generalization of Bochner's tube theorem to functions defined on tube-like domains whose base is not an open set. Theorem Let

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  • In mathematics, Malgrange–Zerner theorem (named for Bernard Malgrange and ) shows that a function on allowing holomorphic extension in each variable separately can be extended, under certain conditions, to a function holomorphic in all variables jointly. This theorem can be seen as a generalization of Bochner's tube theorem to functions defined on tube-like domains whose base is not an open set. Theorem Let and let convex hull of . Let be a locally bounded function such that and that for any fixed point the function is holomorphic in in the interior of for each . Then the function can be uniquely extended to a function holomorphic in the interior of . (en)
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  • In mathematics, Malgrange–Zerner theorem (named for Bernard Malgrange and ) shows that a function on allowing holomorphic extension in each variable separately can be extended, under certain conditions, to a function holomorphic in all variables jointly. This theorem can be seen as a generalization of Bochner's tube theorem to functions defined on tube-like domains whose base is not an open set. Theorem Let (en)
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  • Malgrange–Zerner theorem (en)
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