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An introduction to neutrix composition of distributions and delta function


Kilicman, Adem and Fisher, Brian (2011) An introduction to neutrix composition of distributions and delta function. Malaysian Journal of Mathematical Sciences, 5 (2). pp. 197-209. ISSN 1823-8343; ESSN: 2289-750X


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.

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Additional Metadata

Item Type: Article
Divisions: Faculty of Science
Institute for Mathematical Research
Publisher: Institute for Mathematical Research, Universiti Putra Malaysia
Keywords: Distribution; Delta-function; Composition of distributions; Neutrix; Neutrix limit
Depositing User: Nabilah Mustapa
Date Deposited: 04 Sep 2015 13:02
Last Modified: 04 Sep 2015 13:02
URI: http://psasir.upm.edu.my/id/eprint/38922
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