Integration and microlocal analysis in Colombeau algebras of generalized functions
type: Item
instance of: scholarly article
title: Integration and microlocal analysis in Colombeau algebras of generalized functions
zbMATH Open document ID: 0944.46036
author: Günther Hörmann
published in: Journal of Mathematical Analysis and Applications
publication date: 2000-09-14T00:00:00Z
review text: Generalized functions in the sense of Colombeau extend classical distribution theory to a consistent and efficient method for solving problems in nonlinear analysis. In this paper integration and Fourier transform in the Colombeau algebra \(\mathcal G_r\) of tempered generalized functions are studied. This unifies different settings described by \textit{J. F. Colombeau} [``Elementary introduction to new generalized functions'', North-Holland Math. Stud. 113, Amsterdam, etc. (1985; Zbl 0584.46024)], \textit{M. Nedeljkov} and \textit{S. Pilopovic} [Publ. Inst. Math., Nouv. Sér. 52, 95-104, 105-112 (1992; Zbl 0790.46024 and Zbl 0790.46025)] and \textit{M. Damsma} [Memorandum No. 954, University Twente (1991)]. Some characterizations of regularity for generalized functions are proved. As well the notion of wave front set in the Colombeau algebra \(\mathcal G(\Omega)\), \(\Omega\) an open set of \(\mathbb{R}^n\), is investigated.
Mathematics Subject Classification ID: 46F30
Mathematics Subject Classification ID: 46F05
Mathematics Subject Classification ID: 46T30
zbMATH DE Number: 1384926
zbMATH Keywords: microlocal analysis
zbMATH Keywords: Colombeau algebra
zbMATH Keywords: Schwartz distributions
zbMATH Keywords: integration
zbMATH Keywords: Fourier transform
zbMATH Keywords: regularity for generalized functions
reviewed by: D. Zarnadze
MaRDI profile type: Publication
OpenAlex ID: W2080355891
cites work: Q3709296
cites work: Q3671563
cites work: Q4285393
cites work: Q4220519
cites work: Q4272018
cites work: Q4284926
cites work: Fourier analysis on Colombeau's algebra of generalized functions
DOI: 10.1006/JMAA.1999.6565
description: scientific article; zbMATH DE number 1384926