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An introduction to neutrix composition of distributions and delta function

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 di...

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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
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spelling my.upm.eprints.389222015-09-04T13:02:35Z http://psasir.upm.edu.my/id/eprint/38922/ An introduction to neutrix composition of distributions and delta function Kilicman, Adem Fisher, Brian 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. Institute for Mathematical Research, Universiti Putra Malaysia 2011-07 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/38922/1/38922.pdf 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 http://einspem.upm.edu.my/journal/fullpaper/vol5no2/4.%20adem%20kilicman%20et%20al.pdf
institution Universiti Putra Malaysia
building UPM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Putra Malaysia
content_source UPM Institutional Repository
url_provider http://psasir.upm.edu.my/
language English
description 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.
format Article
author Kilicman, Adem
Fisher, Brian
spellingShingle Kilicman, Adem
Fisher, Brian
An introduction to neutrix composition of distributions and delta function
author_facet Kilicman, Adem
Fisher, Brian
author_sort Kilicman, Adem
title An introduction to neutrix composition of distributions and delta function
title_short An introduction to neutrix composition of distributions and delta function
title_full An introduction to neutrix composition of distributions and delta function
title_fullStr An introduction to neutrix composition of distributions and delta function
title_full_unstemmed An introduction to neutrix composition of distributions and delta function
title_sort introduction to neutrix composition of distributions and delta function
publisher Institute for Mathematical Research, Universiti Putra Malaysia
publishDate 2011
url 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
_version_ 1643832273894637568
score 13.244414

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