An inverse Sturm–Liouville differential operators with a constant delay and transmission conditions

In this paper, we study Sturm-Liouville differential operators with a constant delay and transmission boundary conditions. We establish properties of the spectral characteristics function in the Dirichlet and Dirichlet-Neumann boundary conditions. So, we investigate the inverse problem of recovering operators from their spectra. Also, we construct the potential function by using the Fourier series of the Sturm–Liouville differential operator. The efficiency of the present method are demonstrated through several examples