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A Hartogs-type theorem for solutions to systems with regualr singularities. (English) Zbl 0942.32010

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)].

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
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