A Class of Integral Operators and Bessel Plancherel Transform on Lα2. (1st March 2012)

• Record Type: Journal Article
• Authors: Dziri, M.
• Other Names: Jain Pankaj Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2012(2012)
• Publication Date: 2012-03-01
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2012/419578
• Languages: English
• ISSNs: 0972-6802

Abstract

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.