Interpolation by weighted Paley–Wiener spaces associated with the Dunkl transform

Given α>−12, σ>0σ>0 and 1⩽p<∞1⩽p<∞, we study the interpolation problem in the space PWσp,α of entire functions f:C→Cf:C→C of exponential type ⩽σ   for which ∫R|f(x)|p×|x|2α+1dx<∞, with nodes of interpolation at sj/σsj/σ, j∈Zj∈Z, where {sj:j∈N}{sj:j∈N} is the increasing sequence of all positive roots of the Bessel function Jα+1(z)Jα+1(z) of order α+1α+1, and sj=−s−jsj=−s−j for all j∈Zj∈Z. We prove that if 4(α+1)2α+3:=p1(α)