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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| Format: | Article |
| Language: | English |
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Institute for Mathematical Research, Universiti Putra Malaysia
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/38922/ http://psasir.upm.edu.my/id/eprint/38922/1/38922.pdf |
| _version_ | 1848849005870579712 |
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| author | Kilicman, Adem Fisher, Brian |
| author_facet | Kilicman, Adem Fisher, Brian |
| author_sort | Kilicman, Adem |
| building | UPM Institutional Repository |
| collection | Online Access |
| 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. |
| first_indexed | 2025-11-15T09:43:31Z |
| format | Article |
| id | upm-38922 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T09:43:31Z |
| publishDate | 2011 |
| publisher | Institute for Mathematical Research, Universiti Putra Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-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 |
| spellingShingle | Kilicman, Adem Fisher, Brian An introduction to neutrix composition of distributions and delta function |
| title | 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_short | An introduction to neutrix composition of distributions and delta function |
| title_sort | introduction to neutrix composition of distributions and delta function |
| url | http://psasir.upm.edu.my/id/eprint/38922/ http://psasir.upm.edu.my/id/eprint/38922/ http://psasir.upm.edu.my/id/eprint/38922/1/38922.pdf |