Takeuchi, Kiyoshi A Hartogs-type theorem for solutions to systems with regualr singularities. (English) Zbl 0942.32010 Arch. Math. 73, No. 5, 390-393 (1999). The author proves a Hartogs-type extension theorem for solutions of regular specializable \(\mathcal D_x\)-modules. This theorem can be considered as a natural generalization of a result of Kashiwara-Oshima for higher codimensional cases (and to systems) [M. Kashiwara and T. Oshima, Ann. Math., II. Ser. 106, 145-200 (1977; Zbl 0358.35073)]. The proof essentially relies upon a comparison theorem due to Y. Laurent and T. Monteiro Fernandes [Publ. Res. Inst. Math. Sci. 24, No. 3, 397-431 (1988; Zbl 0704.35032)]. Reviewer: A.V.Chernecky (Odessa) MSC: 32C38 Sheaves of differential operators and their modules, \(D\)-modules 35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs 35S15 Boundary value problems for PDEs with pseudodifferential operators Keywords:\(V\)-filtration; \(\mathcal D_x\)-module; vanishing theorem; Hartogs-type extension theorem Citations:Zbl 0358.35073; Zbl 0704.35032 PDFBibTeX XMLCite \textit{K. Takeuchi}, Arch. Math. 73, No. 5, 390--393 (1999; Zbl 0942.32010) Full Text: DOI