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Topological Structures in Colombeau Algebras: Topological $\widetilde{\mathbb{C}}$ -modules and Duality Theory

Topological Structures in Colombeau Algebras: Topological $\widetilde{\mathbb{C}}$ -modules and... We study modules over the ring $\widetilde{\mathbb{C}}$ of complex generalized numbers from a topological point of view, introducing the notions of $\widetilde{\mathbb{C}}$ -linear topology and locally convex $\widetilde{\mathbb{C}}$ -linear topology. In this context particular attention is given to completeness, continuity of $\widetilde{\mathbb{C}}$ -linear maps and elements of duality theory for topological $\widetilde{\mathbb{C}}$ -modules. As main examples we consider various Colombeau algebras of generalized functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Applicandae Mathematicae Springer Journals

Topological Structures in Colombeau Algebras: Topological $\widetilde{\mathbb{C}}$ -modules and Duality Theory

Acta Applicandae Mathematicae , Volume 88 (1) – Apr 29, 2005

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References (57)

Publisher
Springer Journals
Copyright
Copyright © 2005 by Springer
Subject
Mathematics; Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Complex Systems; Classical Mechanics
ISSN
0167-8019
eISSN
1572-9036
DOI
10.1007/s10440-005-6700-y
Publisher site
See Article on Publisher Site

Abstract

We study modules over the ring $\widetilde{\mathbb{C}}$ of complex generalized numbers from a topological point of view, introducing the notions of $\widetilde{\mathbb{C}}$ -linear topology and locally convex $\widetilde{\mathbb{C}}$ -linear topology. In this context particular attention is given to completeness, continuity of $\widetilde{\mathbb{C}}$ -linear maps and elements of duality theory for topological $\widetilde{\mathbb{C}}$ -modules. As main examples we consider various Colombeau algebras of generalized functions.

Journal

Acta Applicandae MathematicaeSpringer Journals

Published: Apr 29, 2005

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