Open AccessA Generalization of Bochner's Tube Theorem in Elliptic Boundary Value Problems
Author(s) -
Motoo Uchida
Publication year - 1995
Publication title -
publications of the research institute for mathematical sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.786
H-Index - 39
eISSN - 1663-4926
pISSN - 0034-5318
DOI - 10.2977/prims/1195163597
Subject(s) - mathematics , holomorphic function , pure mathematics , submanifold , open mapping theorem (functional analysis) , sheaf , mathematical analysis , complexification , danskin's theorem , implicit function theorem , brouwer fixed point theorem , banach space , fixed point theorem , eberlein–šmulian theorem , lp space
It is classically well known as Bochner's tube theorem that any holomorphic function defined on a tube domain T in a complex affine space has analytic continuation on the convex full of T [H, Theorem 2.5.10]. Now let M be a real analytic manifold, X its complexification. Let TM X be the normal bundle of M in X, VM the functor of specialization along M, and let J?M denote the sheaf H°vM(&x} on TMX. In [SKK, Chap.I], in connection with the theory of microfunctions, a proof is given to the following local version of Bochner's tube theorem :
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