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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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 |
| Summary: | 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. |
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| ISSN: | 0972-6802 1758-4965 |