An Analog of Titchmarsh's Theorem for the Mehler–Fock Transform

Abstract

In this paper, we introduce a generalized dual translation operator to establish an analogue of Titchmarsh's
and Dini-Lipschitz's theorems for the Mehler-Fock transform. This result is applied to functions
\( f \in L^1\left(I, dx\right) \cap L^2\left(I, dx\right) \), where \( I = \left[1, +\infty\right) \)