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Zbl 0753.35005
Bony, J.-M.; Lerner, N.
Quantification asymptotique et microlocalisations d'ordre supérieur. I. (French)
[J] Ann. Sci. Éc. Norm. Supér. (4) 22, No. 3, 377-433 (1989). ISSN 0012-9593

This paper presents a complete and deep investigation of the so called $k$-microlocalization. The authors develop a microlocal calculus of higher order studying $k$-microdifferential operators, $k$-microlocal regularity and other geometric and analytic topics of the microlocal analysis generalizing the usual (first order) microlocalization. The exposition is technical but the authors have the intention to build a $k$-microlocal calculus which can be easily applied to the analysis of different problems and in particular for the examination of the propagation of singularities for nonlinear problems. The previous second and third order microlocalizations are considered as examples and the link with other higher order microlocalizations is discussed.
[C.M.Brauner (Bordeaux)]

MSC 2000:: *35A27 Sheaf-theoretic methods (PDE)
35L67 Shocks, etc.

Keywords: $k$-microdifferential operators; $k$-microlocal regularity; propagation of singularities; nonlinear problems; higher order microlocalizations

Citations: Zbl 0627.35065; Zbl 0669.35073

Cited in: Zbl 0799.35017 Zbl 0758.35004

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