A Class of Integral Operators and Bessel Plancherel Transform on 𝐿𝟐𝜶
For the relation between Bessel Plancherel transform and a wide class of integral operators we establish some results generalizing the corresponding results for the cosine transform, given by Goldberg (1972) and Titchmarsh (1937). Building on these results we obtain a new properties of certain well...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2012/419578 |
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| _version_ | 1849695925180563456 |
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| author | M. Dziri |
| author_facet | M. Dziri |
| author_sort | M. Dziri |
| collection | DOAJ |
| description | For the relation between Bessel Plancherel transform and a wide class of integral operators we establish some results generalizing the corresponding results for the cosine transform, given by Goldberg (1972) and Titchmarsh (1937). Building on these results we obtain a new properties of certain well-known integral transforms associated with the eigenfunction of the Bessel
differential operator defined on (0, ∞) by 𝑙𝛼𝑢=𝑢+((2𝛼+1)/𝑥)𝑢, 𝛼>−1/2. We also construct a class of integral operators which commute with Bessel Plancherel transform. |
| format | Article |
| id | doaj-art-d0dfd395e52a4e83b7bb92f9a2d2c612 |
| institution | DOAJ |
| issn | 0972-6802 1758-4965 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-d0dfd395e52a4e83b7bb92f9a2d2c6122025-08-20T03:19:35ZengWileyJournal of Function Spaces and Applications0972-68021758-49652012-01-01201210.1155/2012/419578419578A Class of Integral Operators and Bessel Plancherel Transform on 𝐿𝟐𝜶M. Dziri0Department of Mathematics, Faculty of Sciences of Tunis, Tunis 2092, TunisiaFor the relation between Bessel Plancherel transform and a wide class of integral operators we establish some results generalizing the corresponding results for the cosine transform, given by Goldberg (1972) and Titchmarsh (1937). Building on these results we obtain a new properties of certain well-known integral transforms associated with the eigenfunction of the Bessel differential operator defined on (0, ∞) by 𝑙𝛼𝑢=𝑢+((2𝛼+1)/𝑥)𝑢, 𝛼>−1/2. We also construct a class of integral operators which commute with Bessel Plancherel transform.http://dx.doi.org/10.1155/2012/419578 |
| spellingShingle | M. Dziri A Class of Integral Operators and Bessel Plancherel Transform on 𝐿𝟐𝜶 Journal of Function Spaces and Applications |
| title | A Class of Integral Operators and Bessel Plancherel Transform on 𝐿𝟐𝜶 |
| title_full | A Class of Integral Operators and Bessel Plancherel Transform on 𝐿𝟐𝜶 |
| title_fullStr | A Class of Integral Operators and Bessel Plancherel Transform on 𝐿𝟐𝜶 |
| title_full_unstemmed | A Class of Integral Operators and Bessel Plancherel Transform on 𝐿𝟐𝜶 |
| title_short | A Class of Integral Operators and Bessel Plancherel Transform on 𝐿𝟐𝜶 |
| title_sort | class of integral operators and bessel plancherel transform on 𝐿𝟐𝜶 |
| url | http://dx.doi.org/10.1155/2012/419578 |
| work_keys_str_mv | AT mdziri aclassofintegraloperatorsandbesselplanchereltransformonl2α AT mdziri classofintegraloperatorsandbesselplanchereltransformonl2α |