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Title: On duality theory and pseudodifferential techniques for Colombeau algebras: generalized delta functionals, kernels and wave front sets
Authors: Garetto, Claudia
Hormann, Gunther
Keywords: Colombeau generalized functions
Duality theory
Pseudodifferential operators
Microlocal analysis
Issue Date: 2006
Publisher: © Mathematical Institute of the Serbian Academy of Science and Arts
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.
Abstract: 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.
Description: 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.
Sponsor: GH was supported by FWF grant P16820-N04
Version: Submitted for publication
URI: https://dspace.lboro.ac.uk/2134/17307
Publisher Link: http://www.emis.de/journals/BSANU/index.html
ISSN: 0561-7332
Appears in Collections:Closed Access (Maths)

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