On analogue of Jordan–Dirichlet theorem about the convergence of the expansions in eigenfunctions of a certain class of differential-difference operators

An analogue of Jordan–Dirichlet theorem is established of convergence of the expansions in eigen functions of the operator $Ly=\alpha y'(x)-y'(1-x)$ with the boundary condition $U(y)=ay(0)+by(1)-(y,\varphi)=0$.