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Multi-specialization and multi-asymptotic expansions. (English) Zbl 1231.32008

Summary: We extend the notion of specialization functor to the case of several closed submanifolds satisfying some suitable conditions. Applying this functor to the sheaf of Whitney holomorphic functions we construct different kinds of sheaves of multi-asymptotically developable functions, whose definitions are natural extensions of the definition of strongly asymptotically developable functions introduced by H. Majima [Asymptotic analysis for integrable connections with irregular singular points. Lect. Notes Math. 1075. Berlin: Springer (1984; Zbl 0546.58003)].

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
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.)
34M30 Asymptotics and summation methods for ordinary differential equations in the complex domain

Citations:

Zbl 0546.58003
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References:

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