The sharp topology on the full Colombeau algebra of generalized functions

In this paper, we define natural and intrinsic metrizable topologies ℑ Ω , ℑ s, Ω , ℑ and ℑ s on (Ω), s (Ω), and , respectively. This allows us to speak of approximation and convergence in these algebras. The topologies induced by ℑ Ω on s (Ω) and by ℑ on coincide with Scarpalezos's sharp topol...

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Bibliographic Details
Published in:Integral transforms and special functions 2006-02, Vol.17 (2-3), p.165-170
Main Authors: Aragona, J., Fernandez, R., Juriaans, S. O.
Format: Article
Language:English
Subjects:
Colombeau algebra
Generalized function
Sharp topologies
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Summary:In this paper, we define natural and intrinsic metrizable topologies ℑ Ω , ℑ s, Ω , ℑ and ℑ s on (Ω), s (Ω), and , respectively. This allows us to speak of approximation and convergence in these algebras. The topologies induced by ℑ Ω on s (Ω) and by ℑ on coincide with Scarpalezos's sharp topologies.
ISSN:1065-2469
1476-8291
DOI:10.1080/10652460500437864