A Class of Integral Operators and Bessel Plancherel Transform on 𝐿𝟐𝜶 - M. Dziri (Journal of Function Spaces and Applications, 2012)
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.