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Quantification asymptotique et microlocalisations d’ordre supérieur. I. (French) Zbl 0753.35005
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.

MSC:
35A27 Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs
35L67 Shocks and singularities for hyperbolic equations
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