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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.

##### MSC:
 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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