UNIFORM CONVERGENCE OF EXPANSIONS IN THEFOURIER SERIES IN THE SYSTEM OF ROOT FUNCTIONSOF SOME FOURTH-ORDER SPECTRAL PROBLEM

In this paper we consider an eigenvalue problem for ordinary differential equations of fourth order with a spectral parameter in three of the boundary conditions.This problem describes small bending vibrations of a homogeneous Euler-Bernoulli beam of constant rigidity, in the cross sections of which a longitudinal force acts, at the left end of which a load is concentrated, and at the right end an inertial load is concentrated.Sufficient conditions are established for the uniform convergence of expansions in the Fourier series in the system of root functions of this spectral problem.