Electronic Journal of Differential Equations,
Vol. 2012 (2012), No. 87, pp. 1-20.
Title: Generalized Heaviside functions in the Colombeau theory context
Author: Francisco Villarreal (FEIS-UNESP, Sao Paulo, Brazil)
Abstract:
We defined generalized Heaviside functions for a variable x
in $\mathbb{R}^n$, and for variables (x,t) in
$\mathbb{R}^n\times\mathbb{R}^m$. Then study properties such as:
composition, invertibility, and association relation (the weak equality).
This work is developed in the Colombeau generalized functions context.
Submitted November 1, 2011. Published June 04, 2012.
Math Subject Classifications: 46F30, 35G20.
Key Words: Generalized function; Heaviside function; distribution.