Generalization of Titchmarsh's Theorem in the space L^2(R, A_{alpha, beta}(x)dx)

Abstract

In this paper, using a generalized Jacobi-Dunkl translation operator, we prove an analog of Titchmarsh's theorem for functions satisfying the φ-Jacobi-Dunkl Lipschitz condition in L²(ℝ, A_α,β(x)dx), α ≥ β ≥ -1 ∕ 2, α ≠ -1 ∕ 2.