A Class of Integral Operators and Bessel Plancherel Transform on Lα2. (1st March 2012) - Dziri, M.
Abstract : 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 l α u = u ′′ + ( ( 2 α + 1 ) / x ) u ′, α > − 1 / 2 . We also construct a class of integral operators which commute with Bessel Plancherel transform.