Regular rapidly decreasing nonlinear generalized functions. Application to microlocal regularityReportar como inadecuado




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1 CRREF - Centre de recherches et de ressources en éducation et formation 2 AOC - Analyse Optimisation Controle

Abstract : We present new types of regularity for nonlinear generalized functions, based on the notion of regular growth with respect to the regularizing parameter of Colombeau-s simplified model. This generalizes the notion of G^{ \infty }-regularity introduced by M. Oberguggenberger. A key point is that these regularities can be characterized, for compactly supported generalized functions, by a property of their Fourier transform. This opens the door to microanalysis of singularities of generalized functions, with respect to these regularities. We present a complete study of this topic, including properties of the Fourier transform exchange and regularity theorems and relationship with classical theory, via suitable results of embeddings.

Keywords : microlocal regularity Colombeau generalized functions rapidly decreasing generalized functions Fourier transform





Autor: Antoine Delcroix -

Fuente: https://hal.archives-ouvertes.fr/



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