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On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets

journal contribution
posted on 20.04.2015, 10:11 by Claudia Garetto, Gunther Hormann
Summarizing basic facts from abstract topological modules over Colombeau generalized complex numbers we discuss duality of Colombeau algebras. In particular, we focus on generalized delta functionals and operator kernels as elements of dual spaces. A large class of examples is provided by pseudodifferential operators acting on Colombeau algebras. By a refinement of symbol calculus we review a new characterization of the wave front set for generalized functions with applications to microlocal analysis.

Funding

GH was supported by FWF grant P16820-N04

History

School

  • Science

Department

  • Mathematical Sciences

Citation

GARETTO, C. and HORMANN, G., 2005. On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets. Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences Mathématiques, 133 (31), pp. 115-136.

Publisher

© Mathematical Institute of the Serbian Academy of Science and Arts

Version

SMUR (Submitted Manuscript Under Review)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2006

Notes

This article is closed access. It was presented at the conference, Generalised Functions 2004: Topics in PDE, Harmonic Analysis and Mathematical Physics, Novi Sad, 22nd-28th September 2004.

ISSN

0561-7332

Language

en