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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| Language: | English |
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Hindawi Limited
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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doaj-d0dfd395e52a4e83b7bb92f9a2d2c6122020-11-24T20:48:56ZengHindawi LimitedJournal 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
M. Dziri |
| spellingShingle |
M. Dziri A Class of Integral Operators and Bessel Plancherel Transform on 𝐿𝟐𝜶 Journal of Function Spaces and Applications |
| author_facet |
M. Dziri |
| author_sort |
M. Dziri |
| title |
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_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_sort |
class of integral operators and bessel plancherel transform on 𝐿𝟐𝜶 |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces and Applications |
| issn |
0972-6802 1758-4965 |
| publishDate |
2012-01-01 |
| 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. |
| url |
http://dx.doi.org/10.1155/2012/419578 |
| work_keys_str_mv |
AT mdziri aclassofintegraloperatorsandbesselplanchereltransformonl2α AT mdziri classofintegraloperatorsandbesselplanchereltransformonl2α |
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1716807388394160128 |