Generalization of Titchmarsh's Theorem for the generalized Fourier transform in the space L^2_{alpha,beta}(R)

Abstract

In this paper, we prove the generalization of Titchmarsh's theorem for the generalized Fourier transform for functions satisfying the (ψ, 2, k)-Cherednik-Opdam Lipschitz condition in the space L²_{α, β}(ℝ).