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

Claudia Garetto
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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.

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Claudia Garetto. 2006-01-09. Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity. https://arxiv.org/abs/math/0511297

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