Convergence of expansions for eigenfunctions and asymptotics of the spectral data of the Sturm-Liouville problem

Abstract

Uniform convergence of the expansion of an absolutely continuous function for eigenfunctions of the Sturm-Liouville problem $-y"+q\left(x\right)y=\mu y,$ $y\left(0\right)=0,$ $y\left(\pi \right)\cos \beta +y^{\prime }\left(\pi \right)\sin \beta =0,$ $\beta \in \left(0,\pi \right)$ with summable potential $q\in L_{\mathbb{R}}^1\left[0,\pi \right]$ is proved. This result is used to obtain more precise asymptotic formulae for eigenvalues and norming constants of this problem.

14 pages, in Russian