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Tempered microlocalization. (Microlocalisation tempérée.) (French) Zbl 0805.58059
The theory of microfunction and \(\mathcal D\)-module is one of the big works by M. Sato and M. Kashiwara. In particular, Kashiwara is a main constructor of the theory, and the fruit of his work has appeared in many papers and books in 1970-1990. In the present book, the author builds the theory of “tempered” microlocalization of distributions and holomorphic functions. Hyperfunctions and their microlocalization are an ultimate generalization of the concept of functions. However, solutions of a regular holonomic system are contained in a more narrow class of function space. Many important concrete functions are solutions of regular (holonomic) \(\mathcal D\)-modules. Tempered microlocalization is essential in analyzing the microlocal structure of regular \(\mathcal D\)-modules. The author gives new sheaves of microlocalizations and microdifferential operators, invariant under complex canonical transformations. We can apply these new tools to the study of distribution solutions of linear systems, in the systematic way that has been achieved in hyperfunction theory.
Reviewer: M.Muro (Yanagido)

MSC:
58J15 Relations of PDEs on manifolds with hyperfunctions
32A45 Hyperfunctions
32C38 Sheaves of differential operators and their modules, \(D\)-modules
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