An introduction to neutrix composition of distributions and delta function

• Main Authors: Kilicman, Adem, Fisher, Brian
• Format: Article
• Language: English
• Published: Institute for Mathematical Research, Universiti Putra Malaysia 2011
• Online Access: http://psasir.upm.edu.my/id/eprint/38922/1/38922.pdf; http://psasir.upm.edu.my/id/eprint/38922/; http://einspem.upm.edu.my/journal/fullpaper/vol5no2/4.%20adem%20kilicman%20et%20al.pdf
• Institution: Universiti Putra Malaysia

The composition of the distribution g(s) (x) and an infinitely differentiable function f (x) having a simple zero at the point x = x0 is defined by Gel’fand Shilov by the equation g(s) (f (x)). It is shown how this definition can be extended to functions f (x) which are not necessarily infinitely differentiable or not having simple zeros at the point x = x0, by defining g(s) (f (x)) as the limit or neutrix limit of the sequence {g(s)n (f(x))} where {gn (x)} is a certain sequence of infinitely differentiable functions converging to the Dirac delta-function g(x). A number of examples are given.