Equiconvergence of expansions in eigenfunctions of Sturm-Liouville operators with distributional potentials in Hölder spaces

Abstract

We establish the equiconvergence of expansions of an arbitrary function in the class L2(0, π) in the Fourier series in sines and in the Fourier series in the eigenfunctions of the first boundary value problem for the one-dimensional Schrodinger operator with a nonclassical potential. The equiconvergence is studied in the norm of the Holder space. The potential is the derivative of a function that belongs to a fractional-order Sobolev space.