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Acta Applicandae Mathematica

, Volume 88, Issue 1, pp 81–123 | Cite as

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

  • Claudia Garetto
Article

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.

Keywords

modules over the ring of complex generalized numbers algebras of generalized functions topology duality theory 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di TorinoTorinoItalia

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