The Range of the Spectral Projection Associated with the Dunkl Laplacian. (24th July 2020)

• Record Type: Journal Article
• Authors: Ben Said, Salem; Mejjaoli, Hatem
• Other Names: Sugimoto Mitsuru Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2020(2020)
• Publication Date: 2020-07-24
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2020/7803719
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : For s ∈ ℝ, denote by P k s f the "projection" of a function f in D ℝ d into the eigenspaces of the Dunkl Laplacian Δ k corresponding to the eigenvalue − s 2 . The parameter k comes from Dunkl's theory of differential-difference operators. We shall characterize the range of P k s on the space of functions f ∈ D ℝ d supported inside the closed ball B O, R ¯ . As an application, we provide a spectral version of the Paley-Wiener theorem for the Dunkl transform.