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Topological structures in Colombeau algebras: topological ℂ̃-modules and duality theory

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journal contribution
posted on 20.04.2015, 11:17 by Claudia Garetto
We study modules over the ring ℂ̃ of complex generalized numbers from a topological point of view, introducing the notions of ℂ̃-linear topology and locally convex ℂ̃-linear topology. In this context particular attention is given to completeness, continuity of ℂ̃-linear maps and elements of duality theory for topological ℂ̃-modules. As main examples we consider various Colombeau algebras of generalized functions. © Springer 2005.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Acta Applicandae Mathematicae

Volume

88

Issue

1

Pages

81 - 123

Citation

GARETTO, C., 2005. Topological structures in Colombeau algebras: topological ℂ̃-modules and duality theory. Acta Applicandae Mathematicae, 88 (1), pp. 81 - 123

Publisher

© Springer

Version

AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2005

Notes

This article was published in the journal, Acta Applicandae Mathematicae [© Springer]. The final publication is available at Springer via http://dx.doi.org/10.1007/s10440-005-6700-y

ISSN

0167-8019

Language

en