On the Hilbert transform in the framework of generalized functions

DOI10.1080/10652469.2011.613381zbMath1269.46026OpenAlexW2051186544MaRDI QIDQ3166781

Jorge Aragona, H. Panzarelli, Roseli Fernandez

Publication date: 15 October 2012

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

Full work available at URL: https://doi.org/10.1080/10652469.2011.613381

zbMATH Keywords

Hilbert transformColombeau algebratempered generalized function

Mathematics Subject Classification ID

Integral transforms in distribution spaces (46F12) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) (46F30)

Cites Work

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• On the Hamilton-Jacobi equation in the framework of generalized functions
• Generalized Hilbert transforms in tempered distributions
• Natural topologies on Colombeau algebras
• Intrinsic definition of the Colombeau algebra of generalized functions
• A discontinuous Colombeau differential calculus
• Distributional boundary value theorems and Hilbert transforms
• The Hilbert problem for generalized functions
• Fourier analysis on Colombeau's algebra of generalized functions
• Algebraic and Geometric Theory of the Topological Ring of Colombeau Generalized Functions
• The Hilbert Transform of Generalized Functions and Applications
• Hilbert Transforms, Plemelj Relations, and Fourier Transforms of Distributions

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