The continuous Jacobi transform
The purpose of this paper is to define the continuous Jacobi transform as an extension of the discrete Jacobi transform. The basic properties including the inversion theorem for the continuous Jacobi transform are studied. We also derive an inversion formula for the transform which maps L1(R+) into...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1983-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171283000137 |
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| _version_ | 1832552780319948800 |
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| author | E. Y. Deeba E. L. Koh |
| author_facet | E. Y. Deeba E. L. Koh |
| author_sort | E. Y. Deeba |
| collection | DOAJ |
| description | The purpose of this paper is to define the continuous Jacobi transform as an extension of the discrete Jacobi transform. The basic properties including the inversion theorem for the continuous Jacobi transform are studied. We also derive an inversion formula for the transform which maps L1(R+) into Lw2(−1,1) where w(x)=(1−x)α(1+x)β. |
| format | Article |
| id | doaj-art-6cebb28d6af44356ba3007ea4c0c9f09 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1983-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-6cebb28d6af44356ba3007ea4c0c9f092025-02-03T05:57:46ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251983-01-016114516010.1155/S0161171283000137The continuous Jacobi transformE. Y. Deeba0E. L. Koh1Department of Mathematical Sciences, University of Petroleum and Minerals, Dhahran, Saudi ArabiaDepartment of Mathematics and Statistics, University of Regina, Regina S4S 4J5, CanadaThe purpose of this paper is to define the continuous Jacobi transform as an extension of the discrete Jacobi transform. The basic properties including the inversion theorem for the continuous Jacobi transform are studied. We also derive an inversion formula for the transform which maps L1(R+) into Lw2(−1,1) where w(x)=(1−x)α(1+x)β.http://dx.doi.org/10.1155/S0161171283000137continuous Jacobi transformdiscrete Jacobi transformcontinuous Legendre transforminverse Jacobi transform. |
| spellingShingle | E. Y. Deeba E. L. Koh The continuous Jacobi transform International Journal of Mathematics and Mathematical Sciences continuous Jacobi transform discrete Jacobi transform continuous Legendre transform inverse Jacobi transform. |
| title | The continuous Jacobi transform |
| title_full | The continuous Jacobi transform |
| title_fullStr | The continuous Jacobi transform |
| title_full_unstemmed | The continuous Jacobi transform |
| title_short | The continuous Jacobi transform |
| title_sort | continuous jacobi transform |
| topic | continuous Jacobi transform discrete Jacobi transform continuous Legendre transform inverse Jacobi transform. |
| url | http://dx.doi.org/10.1155/S0161171283000137 |
| work_keys_str_mv | AT eydeeba thecontinuousjacobitransform AT elkoh thecontinuousjacobitransform AT eydeeba continuousjacobitransform AT elkoh continuousjacobitransform |