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.