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

摘要

We establish the equiconvergence of expansions of an arbitrary function in the class L 2(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 Schrödinger operator with a nonclassical potential. The equiconvergence is studied in the norm of the Hölder space. The potential is the derivative of a function that belongs to a fractional-order Sobolev space.