Topological Structures in Colombeau Algebras: Investigation of the Duals of ${\cal G}_{{\rm c}}(\Omega)$, ${\cal G}(\Omega)$ and ${\cal G}_{{\cal S}}({\Bbb R}^n)$

By Claudia Garetto. 2005

55 citations recorded by the source corpus.

Abstract.We study the topological duals of the Colombeau algebras ${\cal G}_{{\rm c}}(\Omega)$, ${\cal G}(\Omega)$ and ${\cal G}_{{\cal S}}({\Bbb R}^n)$, discussing some continuous embeddings and the properties of generalized delta functionals.

Subfields: Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9524a07bae625f7b50757bf7005a7d2ad78cea46

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In Mathematical Physics

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

Citations in the corpus

• Internal sets and internal functions in Colombeau theory (2007, unknown): “09 94 v1 [ m at h. FA ] 6 J ul 2 00”
• Pseudodifferential operators with generalized symbols and regularity theory (2005, methodology): “As an application, we formulate a sufficient condition of hypoellipticity in this setting, which leads to regularity results for generalized pseudodifferential equations.”