A Class of Integral Operators and Bessel Plancherel Transform on Lα2

الملخص EN

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.