Dirac delta and singular distributions: The general non-good function case
A rigorous approach for defining Dirac type singular distributions is detailed for the case where the distribution is to be applied to functions that are normally to be considered in physical applications and which are outside formal distribution theory. Four principles that underpin singular distri...
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| Format: | Conference Paper |
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Conference organizer
2012
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| Online Access: | http://hdl.handle.net/20.500.11937/42024 |
| _version_ | 1848756304635494400 |
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| author | Howard, Roy |
| author2 | Publication managed by conference programme committee |
| author_facet | Publication managed by conference programme committee Howard, Roy |
| author_sort | Howard, Roy |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | A rigorous approach for defining Dirac type singular distributions is detailed for the case where the distribution is to be applied to functions that are normally to be considered in physical applications and which are outside formal distribution theory. Four principles that underpin singular distributions are detailed. The approach is applied to examples in the recent literature and the limitations of several conclusions is made clear. A non-linear distribution which extracts the number of zero crossings of a function is defined. |
| first_indexed | 2025-11-14T09:10:04Z |
| format | Conference Paper |
| id | curtin-20.500.11937-42024 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:10:04Z |
| publishDate | 2012 |
| publisher | Conference organizer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-420242017-02-28T01:39:37Z Dirac delta and singular distributions: The general non-good function case Howard, Roy Publication managed by conference programme committee generalized function singularity Dirac delta distribution zero crossing A rigorous approach for defining Dirac type singular distributions is detailed for the case where the distribution is to be applied to functions that are normally to be considered in physical applications and which are outside formal distribution theory. Four principles that underpin singular distributions are detailed. The approach is applied to examples in the recent literature and the limitations of several conclusions is made clear. A non-linear distribution which extracts the number of zero crossings of a function is defined. 2012 Conference Paper http://hdl.handle.net/20.500.11937/42024 Conference organizer restricted |
| spellingShingle | generalized function singularity Dirac delta distribution zero crossing Howard, Roy Dirac delta and singular distributions: The general non-good function case |
| title | Dirac delta and singular distributions: The general non-good function case |
| title_full | Dirac delta and singular distributions: The general non-good function case |
| title_fullStr | Dirac delta and singular distributions: The general non-good function case |
| title_full_unstemmed | Dirac delta and singular distributions: The general non-good function case |
| title_short | Dirac delta and singular distributions: The general non-good function case |
| title_sort | dirac delta and singular distributions: the general non-good function case |
| topic | generalized function singularity Dirac delta distribution zero crossing |
| url | http://hdl.handle.net/20.500.11937/42024 |