Description of unconditional bases formed by values of the Dunkl kernels

Abstract

Unconditional bases of the form {d _α (iλ _n t) : λ _n ∈ Λ} in the space L ₂(−a, a) with measure |x|^γ dx, γ = 2α + 1, are described. Here d _α (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 J _α is the Bessel function of the first kind.