Asymptotic extension of topological modules and algebras

DOI10.1080/10652460802565040zbMath1179.46042OpenAlexW1990351086MaRDI QIDQ3619815

Maximilian F. Hasler

Publication date: 9 April 2009

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460802565040

zbMATH Keywords

sequence spacegeneralized functiontopological module

Mathematics Subject Classification ID

Normed modules and Banach modules, topological modules (if not placed in 13-XX or 16-XX) (46H25) Other ``topological linear spaces (convergence spaces, ranked spaces, spaces with a metric taking values in an ordered structure more general than (mathbb{R}), etc.) (46A19) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Related Items (5)

Singular solutions to equations of fluid mechanics and dynamics near a Hurricane's eye ⋮ Geometry of balanced and absorbing subsets of topological modules ⋮ The category of Colombeau algebras ⋮ Topology and functoriality in \((\mathcal {C, E, P})\)-algebras. Application to singular differential problems ⋮ Multidimensional asymptotic spectral analysis and applications

Cites Work

• A nonlinear theory of generalized functions.
• Topological structures in Colombeau algebras: Topological \(\widetilde{\mathbb C}\)-modules and duality theory
• Topological structures in Colombeau algebras: Investigation of the duals of \(\mathcal G_c(\Omega)\), \(\mathcal G(\Omega)\) and \(\mathcal G_{\mathcal S}(\mathbb R^n)\)
• Generalized Gevrey Ultradistributions and their Microlocal Analysis
• Embeddings of ultradistributions and periodic hyperfunctions in Colombeau type algebras through sequence spaces
• New Generalized Functions and C^∞ Functions with Values in Generalized Complex Numbers
• Generalized function algebras as sequence space algebras
• Generalized functions as sequence spaces with ultranorms
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