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

By Claudia Garetto. 2005

79 citations recorded by the source corpus.

AbstractWe 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.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d8ef8eea9aa370eee4f3dcb63bb57dced80a8e38

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In Mathematical Physics

1. Todor Gramchev
2. Michael Oberguggenberger
3. Claudia Garetto
4. G. Hörmann

Citations in the corpus

• Pseudodifferential operators with generalized symbols and regularity theory (2005, background): “Further studies of kernel operators in Colombeau algebras including topological investigations are carried out in [9, 12 , 13].”