The Range of the Spectral Projection Associated with the Dunkl Laplacian. (24th July 2020) - Ben Said, Salem; Mejjaoli, Hatem
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.