On the equiconvergence rate of trigonometric series expansions and eigenfunction expansions for the Sturm-Liouville operator with a distributional potential

We study the Sturm-Liouville operator L = -d(2)/dx(2)+ q(x) in the space L-2[0, pi] with the Dirichlet boundary conditions. We assume that the potential has the form q(x) = u'(x), u is an element of W-2(theta)[0, pi], 0 < theta < 1/2. We consider the problem on the uniform (on the entire interval [0, pi]) equiconvergence of the expansion of a function f(x) in a series in the system of root functions of the operator L with its Fourier expansion in the system of sines. We show that if the antiderivative u(x) of the potential belongs to any of the spaces W-2(theta)[0, pi], 0 < theta < 1/2, then the equiconvergence rate can be estimated uniformly over the ball u(x) is an element of B-R = {v(x) is an element of W-2(theta)[0, pi] parallel to nu parallel to w(2)(theta) <= R} for any function f(x) is an element of L (2)[0, pi].