A generalized inversion formula for the continuous Jacobi transform
In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic function F(λ) in Reλ>0 to be the continu...
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| Format: | Article |
| Language: | English |
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Wiley
1987-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171287000796 |
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| _version_ | 1832545678181531648 |
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| author | Ahmed I. Zayed |
| author_facet | Ahmed I. Zayed |
| author_sort | Ahmed I. Zayed |
| collection | DOAJ |
| description | In this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic function F(λ) in Reλ>0 to be the continuous Jacobi transform of a generalized function. |
| format | Article |
| id | doaj-art-d97ea5a28bd34da7b562e34c987fabf1 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1987-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-d97ea5a28bd34da7b562e34c987fabf12025-02-03T07:25:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251987-01-0110467169210.1155/S0161171287000796A generalized inversion formula for the continuous Jacobi transformAhmed I. Zayed0Department of Mathematics, California Polytechnic State University, San Luis Obispo 93407, CA, USAIn this paper we extend the definition of the continuous Jacobi transform to a class of generalized functions and obtain a generalized inversion formula for it. As a by-product of our technique we obtain a necessary and sufficient condition for an analytic function F(λ) in Reλ>0 to be the continuous Jacobi transform of a generalized function.http://dx.doi.org/10.1155/S0161171287000796continuous Jacobi transformgeneralized functionsinverse Jacobi transform. |
| spellingShingle | Ahmed I. Zayed A generalized inversion formula for the continuous Jacobi transform International Journal of Mathematics and Mathematical Sciences continuous Jacobi transform generalized functions inverse Jacobi transform. |
| title | A generalized inversion formula for the continuous Jacobi transform |
| title_full | A generalized inversion formula for the continuous Jacobi transform |
| title_fullStr | A generalized inversion formula for the continuous Jacobi transform |
| title_full_unstemmed | A generalized inversion formula for the continuous Jacobi transform |
| title_short | A generalized inversion formula for the continuous Jacobi transform |
| title_sort | generalized inversion formula for the continuous jacobi transform |
| topic | continuous Jacobi transform generalized functions inverse Jacobi transform. |
| url | http://dx.doi.org/10.1155/S0161171287000796 |
| work_keys_str_mv | AT ahmedizayed ageneralizedinversionformulaforthecontinuousjacobitransform AT ahmedizayed generalizedinversionformulaforthecontinuousjacobitransform |