An analog of Titchmarsh’s theorem and Dini Lipschitz theorem for the Mehler–Fock–Clifford transform

Using a generalized dual translation operator, we obtain an analog of Titchmarsh’s theorem and the analogu of Dini Lipschitz theorem for the Mehler–Fock–Clifford transform for functions in \(f \in L^1(I;x^{-\frac{1}{2}}dx) \cap L^2(I;x^{-\frac{1}{2}}dx)\) $f\in L^1(I;x^{-\frac{1}{2}}dx)\cap L^2(I;x^{-\frac{1}{2}}dx)$ where \(I=]\frac{1}{4},+\infty [\) $I=]\frac{1}{4},+\infty [$ .