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GENERALIZED HEAVISIDE FUNCTIONS IN THE COLOMBEAU THEORY CONTEXT

Francisco Villarreal

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Abstract

We defined generalized Heaviside functions for a variable x in $mathbb{R}^n$, and for variables (x,t) in $mathbb{R}^nimesmathbb{R}^m$. Then study properties such as: composition, invertibility, and association relation (the weak equality). This work is developed in the Colombeau generalized functions context.

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We defined generalized Heaviside functions for a variable x in $mathbb{R}^n$, and for variables (x,t) in $mathbb{R}^nimesmathbb{R}^m$. Then study properties such as: composition, invertibility, and association relation (the weak equality). This work is developed in the Colombeau generalized functions context.

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Available abstract

We defined generalized Heaviside functions for a variable x in $mathbb{R}^n$, and for variables (x,t) in $mathbb{R}^nimesmathbb{R}^m$. Then study properties such as: composition, invertibility, and association relation (the weak equality). This work is developed in the Colombeau generalized functions context.

Key concepts: Heaviside step function, Mathematics, Generalized function, Context (archaeology), Pure mathematics, Variable (mathematics), Mathematical analysis, Paleontology

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