A generalization of Bochner's tube theorem in elliptic boundary value problems (Q1918531)

It is a classical result 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 hull of \(T\). Let \(M\) be a real analytic manifold, \(X\) its complexification, \(T_MX\) the normal bundle of \(M\) in \(X\), \(\nu_M\) the functor of specialization along \(M\), \(\widetilde{\mathcal A}_M\) the sheaf \(H^0\nu_M({\mathcal O}_X)\) on \(T_MX\). Sato, Kawai and Kashiwara proved the following local version of Bochner's tube theorem: Let \(U\) be an open conic subset of \(T_MX\) with connected fibres, \(\widetilde U\) the convex full of \(U\) in each fibre. Then \[ \Gamma(\widetilde U,\widetilde{\mathcal A}_M)\to \Gamma(U,\widetilde{\mathcal A}_M) \] is an isomorphism. In this paper, considering a real setting, the author proves a similar local version of Bochner's theorem in boundary value problems for elliptic systems of differential equations on a real manifold \(X\).