Uniform Convergence of Expansions in Root Functions of a Differential Operator with Integral Boundary Conditions

Abstract

for a second-order ordinary differential operator with integral boundary conditions on an interval of the real line, we derive conditions for the uniform convergence of the spectral expansion of a function in a series in the system of eigenfunctions and associated functions of the operator. We obtain estimates of the rate of convergence of the series and the rate of equiconvergence of such an expansion of a function and its expansion in the trigonometric Fourier series. We also study the uniform convergence of the expansion of a function in the biorthogonal system.