Equiconvergence of expansions in eigenfunctions of Sturm-Liouville operators with distributional potentials in Hölder spaces (Q1760438)

The paper is concerned with the Sturm-Liouville operator \[ Ly= -\frac{d^2y}{d x^2}+q(x)y \] in the space \(L_2[0,\pi]\) with Dirichlet boundary conditions \(y(0)=y(\pi)=0\), where the potential \(q(x)\) is the derivative of a function \(u(x)\in W_2^{\theta}[0,\pi]\), \(0<\theta<1/2\). The author proves the equiconvergence of the expansion of a function \(f\in L_2[0,\pi]\) as a Fourier series in the system of eigenfunctions and associated functions of the operator \(L\) and the expansion of \(f\) as a Fourier series in sines in the norm of the Hölder space \(C^{\theta}[0,\pi]\), \(0<\theta<1/2\).