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A Paley-Wiener theorem about the spectral parameter, and a support theorem for general types of Dunkl spherical means
For $s\in \mathbb R,$ denote by $\cal P_k^s$ the ``projections of a function $f$ in $\mathcal D(\mathbb R^d)$ into the eigenspaces of the Dunkl Laplacian $\Delta_k$ corresponding to the eigenvalue $-s^2.$ The parameter $k$ comes from Dunkl's theory of differential-difference operators. Wa shall characterize the range of $\cal P_k^s$ on …