Point value characterizations and related results in the full Colombeau algebras documentclass{article}usepackage{amssymb}begin{document}pagestyle{empty}${{mathcal {G}}^e(Omega )}$end{document} and documentclass{article}usepackage{amssymb}begin{document}pagestyle{empty}${{mathcal {G}}^d(Omega )}$end{document} |
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| Authors: | Eduard A. Nigsch |
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| Affiliation: | Fakult?t für Mathematik, University of Vienna, Nordbergstra?e 15, 1090 Wien, Austria. Phone: +43 1 4277 50636, Fax: +43 14277 9506 |
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| Abstract: | We present a point value characterization for elements of the elementary full Colombeau algebra ${mathcal {G}}^e(Omega )$ and the diffeomorphism invariant full Colombeau algebra $mathcal {G}^d(Omega )$. Moreover, several results from the special algebra ${mathcal {G}}^s(Omega )$ about generalized numbers and invertibility are extended to the elementary full algebra. |
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| Keywords: | Diffeomorphism invariant Colombeau algebra point value characterization pointvalues algebras of generalized functions invertibility of generalized functions generalized numbers MSC (2010) 46F30 |
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