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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}
Author(s) -
Nigsch Eduard A.
Publication year - 2013
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.200910280
Subject(s) - omega , mathematics , combinatorics , algebra over a field , mathematical physics , physics , pure mathematics , quantum mechanics
We present a point value characterization for elements of the elementary full Colombeau algebra \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {G}}^e(\Omega )$\end{document} and the diffeomorphism invariant full Colombeau algebra \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\mathcal {G}^d(\Omega )$\end{document} . Moreover, several results from the special algebra \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}${\mathcal {G}}^s(\Omega )$\end{document} about generalized numbers and invertibility are extended to the elementary full algebra.