Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity

2005/11/11 by Claudia Garetto, Garetto, Claudia
Mathematics · #13J99 #35S99 #46A20 #46F30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Mathematical and Theoretical Analysis #math.AP #math.FA #msc:13J99 #msc:35S99 #msc:46A20 #msc:46F30

paper · pdf · doi:10.48550/arxiv.math/0511297

openalex publication_date 2005/11/11 · arxiv created 2006/01/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

We introduce different notions of wave front set for the functionals in the dual of the Colombeau algebra \Gc(\Om) providing a way to measure the \G and the \Ginf- regularity in \LL(\Gc(\Om),\wt\C). For the smaller family of functionals having a ``basic structure'' we obtain a Fourier transform-characterization for this type of generalized wave front sets and results of noncharacteristic \G and \Ginf-regularity.

Citations

• Microlocal hypoellipticity of linear partial differential operators with generalized functions as coefficients

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