Inverse problem for the Sturm–Liouville operator with a frozen argument on the time scale

In this paper, we consider the problem of constructing the potential of the Sturm–Liouville equation with a frozen argument on the time scale by the spectrum of the Dirichlet boundary-value problem, where the time scale consists of two segments and the argument is frozen at the end of the first segment. We obtain the uniqueness theorem and construct an algorithm for solving the inverse problem together with necessary and sufficient conditions for its solvability. The case considered substantially differs from the case of the classical Sturm– Liouville operator with a frozen argument.