Algebraic theory of Colombeau's generalized numbers

DOI10.1016/J.JALGEBRA.2013.03.005zbMath1297.46031OpenAlexW2002833341MaRDI QIDQ2437462

Antônio Ronaldo Gomes Garcia, Stanley Orlando Juriaans, Jorge Aragona

Publication date: 3 March 2014

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2013.03.005

zbMATH Keywords

Colombeau algebraalgebraic structuregeneralized numberssharp topologyfull Colombeau algebra

Mathematics Subject Classification ID

Continuous and differentiable maps in nonlinear functional analysis (46T20) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (3)

Off-diagonal condition ⋮ The ring of Colombeau’s full generalized quaternions ⋮ A nonlinear theory of generalized functions

Cites Work

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• Algebraic and Geometric Theory of the Topological Ring of Colombeau Generalized Functions
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• Characterization of colombeau generalized functions by their pointvalues
• Local properties of Colombeau generalized functions
• Rotation Inveriant Generalized Functioins^∗
• The sharp topology on the full Colombeau algebra of generalized functions
• An existence theorem for an analytic first order PDE in the framework of Colombeau's theory

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