Continuous division of differential operators. (English) Zbl 0977.32009

Hauser, Herwig; Narváez-Macarro, Luis

Ann. Inst. Fourier 51, No. 3, 769-778 (2001).

Summary: We give a new proof of the continuity of division by differential operators with analytic coefficients, originally proved by Z. Mebkhout [J. Reine Angew. Math. 503, 193-236 (1998; Zbl 0910.32011)] and the second author. Our methods come from the proof of the Constant Rank Theorem for analytic maps between power series spaces, given by G. Müller [Publ. Math., Inst. Hautes Étud. Sci. 80, 95-115 (1995; Zbl 0831.58008)] and the first author.

MSC:

32C38	Sheaves of differential operators and their modules, \(D\)-modules
14F10	Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials

Keywords:

differential operators; division theorems; continuity

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