Abstract
Unconditional bases of the form {dα(iλnt) : λn ∈ Λ} in the space L2(−a, a) with measure |x|γdx, γ = 2α + 1, are described. Here dα(ixt) is the Dunkl kernel determined by $$d_\alpha (z) = 2^\alpha \Gamma (\alpha + 1)z^{ - \alpha } (J_\alpha (z) + iJ_{\alpha + 1} (z)), \alpha > - 1,$$ where Jα is the Bessel function of the first kind.
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