Uniform equiconvergence of a Fourier series in eigenfunctions of the first boundary value problem and of a Fourier trigonometric series. (Q1432668)

Consider the boundary value problem \[ y''+ (\lambda+ q(x)) y=0,\quad 0< x<\pi,\quad y(0)= y(\widetilde u)= 0.\tag{*} \] Based on the uniform asymptotics of the eigenfunctions of \((*)\), the authors prove that the convergence of the Fourier series in these eigenfunctions does not depend on the potential \(q\).