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Specialization of formal cohomology and asymptotic expansions. (English) Zbl 0980.32004
Following a work of E. Andronikov [‘Microlocalisation tempérée’, Mém. Soc. Math. Fr., Nouv. Sér. 57 (1994; Zbl 0805.58059)] the author builds a theory of Whitney specialization for \(C^\infty\)-functions and holomorphic functions. To an \(\mathbb{R}\)-constructible sheaf it is associated a \({\mathcal D}\)-module. In particular, the constant sheaf gives the germs of functions asymptotically developable.

32C38 Sheaves of differential operators and their modules, \(D\)-modules
34E05 Asymptotic expansions of solutions to ordinary differential equations
34M30 Asymptotics and summation methods for ordinary differential equations in the complex domain
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