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

Claudia Garetto

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

Analysis of PDEs 2007-05-23 v2 Functional Analysis

Authors: Claudia Garetto

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.

Keywords

colombeau algebra dual generalized wave front set microlocal analysis noncharacteristic regularity basic structure fourier transform characterization

Cite

@article{arxiv.math/0511297,
  title  = {Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity},
  author = {Claudia Garetto},
  journal= {arXiv preprint arXiv:math/0511297},
  year   = {2007}
}

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

Abstract

Keywords

Cite

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