Dunkl symmetric coherent pairs of the second kind of positive measures

Abstract In this contribution we deal with pairs of symmetric linear functionals ({u}, {v}) (u, v) such that the corresponding sequences of monic orthogonal polynomials \Pₙ (x;{ {u}) \}₍ ₀ P n (x ; u) n ≥ 0 and \ Pₙ (x;{ {v}) \}₍ ₀ P n (x ; v) n ≥ 0 are related by T ₏_₍+₁ (x;{ {u}) } ₍+₁=Pₙ (x; {v}) - ₍-₁P₍-₂ (x; {v}), ₍-₁ 0, n 2. T μ P n + 1 (x ; u) μ n + 1 = P n (x ; v) - τ n - 1 P n - 2 (x ; v), τ n - 1 ≠ 0, n ≥ 2. Here T T μ is the standard Dunkl operator in one variable. Such a pair of linear functionals is said to be a symmetric T T μ -coherent pair of the second kind. We give a necessary and sufficient condition in order for a pair of symmetric linear functionals to be a T T