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Fundamental structures and asymptotic microlocalization in sheaves of generalized functions. (English) Zbl 0902.18005
Summary: The usual properties of generalized functions are described by means of two fundamental structures. With those structures we can construct in a general way a sheaf \({\mathcal A}\) of differential algebras containing most of the special cases met in the literature.
The sheaf properties of \({\mathcal A}\) allow us to define a local and microlocal analysis which generalizes the classical one in the distribution theory.

MSC:
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
54B40 Presheaves and sheaves in general topology
46F99 Distributions, generalized functions, distribution spaces
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