Representation of functions as the Post-Widder inversion operator of generalized functions
A study is made of the Post-Widder inversion operator to a class of generalized functions in the sense of distributional convergence. Necessary and sufficient conditions are proved for a given function to have the representation as the rth operate of the Post-Widder inversion operator of generalized...
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| Format: | Article |
| Language: | English |
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Wiley
1984-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171284000399 |
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| author | R. P. Manandhar L. Debnath |
| author_facet | R. P. Manandhar L. Debnath |
| author_sort | R. P. Manandhar |
| collection | DOAJ |
| description | A study is made of the Post-Widder inversion operator to a class of generalized functions in the sense of distributional convergence. Necessary and sufficient conditions are proved for a given function to have the representation as the rth operate of the Post-Widder inversion operator of generalized functions. Some representation theorems are also proved. Certain results concerning the testing function space and its dual are established. A fundamental theorem regarding the existence of the real inversion operator (1.6) with r=0 is proved in section 4. A classical inversion theory for the Post-Widder inversion operator with a few other theorems which are fundamental to the representation theory is also developed in this paper. |
| format | Article |
| id | doaj-art-01eb7337004847979f5dc8ceca5a57d6 |
| institution | DOAJ |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1984-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-01eb7337004847979f5dc8ceca5a57d62025-08-20T03:22:30ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251984-01-017237139610.1155/S0161171284000399Representation of functions as the Post-Widder inversion operator of generalized functionsR. P. Manandhar0L. Debnath1Department of Mathematics, Tribhuwan University, Kirtipur Campus, Kathmandu, NepalDepartment of Mathematics, University of Central Florida, Orlando 32816, Florida, USAA study is made of the Post-Widder inversion operator to a class of generalized functions in the sense of distributional convergence. Necessary and sufficient conditions are proved for a given function to have the representation as the rth operate of the Post-Widder inversion operator of generalized functions. Some representation theorems are also proved. Certain results concerning the testing function space and its dual are established. A fundamental theorem regarding the existence of the real inversion operator (1.6) with r=0 is proved in section 4. A classical inversion theory for the Post-Widder inversion operator with a few other theorems which are fundamental to the representation theory is also developed in this paper.http://dx.doi.org/10.1155/S0161171284000399Post-Widder inversion operatorrepresentation theoremstesting function space and its dualgeneralized functions. |
| spellingShingle | R. P. Manandhar L. Debnath Representation of functions as the Post-Widder inversion operator of generalized functions International Journal of Mathematics and Mathematical Sciences Post-Widder inversion operator representation theorems testing function space and its dual generalized functions. |
| title | Representation of functions as the Post-Widder inversion operator of generalized functions |
| title_full | Representation of functions as the Post-Widder inversion operator of generalized functions |
| title_fullStr | Representation of functions as the Post-Widder inversion operator of generalized functions |
| title_full_unstemmed | Representation of functions as the Post-Widder inversion operator of generalized functions |
| title_short | Representation of functions as the Post-Widder inversion operator of generalized functions |
| title_sort | representation of functions as the post widder inversion operator of generalized functions |
| topic | Post-Widder inversion operator representation theorems testing function space and its dual generalized functions. |
| url | http://dx.doi.org/10.1155/S0161171284000399 |
| work_keys_str_mv | AT rpmanandhar representationoffunctionsasthepostwidderinversionoperatorofgeneralizedfunctions AT ldebnath representationoffunctionsasthepostwidderinversionoperatorofgeneralizedfunctions |