Convergence of Eigenfunction Expansions of a Differential Operator with Integral Boundary Conditions

For a second-order ordinary differential operator on an interval of the real line with integral boundary conditions, conditions for the unconditional basis property and uniform convergence of the expansion of a function in terms of the eigen- and associated functions of this operator are established. The convergence and equiconvergence rates of this expansion and the equiconvergence rate of the trigonometric Fourier expansion of this function are estimated. The uniform convergence of its expansion in the adjoint system is studied.