Topological Isomorphism of the Space of Fréchet Generalised Functions.

Ijeoma E. Nwachukwu

doi:10.52589/AJMSS-IICISLI0

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Topological Isomorphism of the Space of Fréchet Generalised Functions.

Publication Date: 2025-09-02

DOI: 10.52589/AJMSS-IICISLI0

Volume/Issue: Volume 8, Issue 3 (2025)

Page No: 247 - 254

Journal: African Journal of Mathematics and Statistics Studies

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Abstract:

The characterisation of the space of Fréchet generalised functions was established with respect to the weak-⋆ topology, which confirms the completeness of the space, G_X, through the space of test functions , D(X). The isomorphism bridges the gap between the Fréchet space of test functions and the space of generalised functions.

Keywords:Generalised FunctionsFréchet SpacesTest FunctionsWeak ⋆ -topologyIsomorphism.

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Copyrights

Authors retain copyright in their articles and have unrestricted rights to reuse, republish, archive, share, and distribute their work after publication.
All articles are published open access under the Creative Commons Attribution 4.0 International (CC BY 4.0) licence, which permits use, sharing, adaptation, distribution, and reproduction in any medium or format, including for commercial purposes, provided appropriate credit is given to the original author(s) and source.