Convergence of expansions for eigenfunctions and asymptotics of the spectral data of the Sturm-Liouville problem
Uniform convergence of the expansion of an absolutely continuous function for eigenfunctions of the Sturm-Liouville problem $-y" + q \left( x \right) y = μy,$ $y \left(0\right)=0,$ $y\left( π\right)\cos β+ y'\left( π\right)\sin β= 0,$ $β\in \left( 0, π\right)$ with summable potential $q \in L_{\mathbb{R}}^1 \left[0, π\right]$ is proved. This result is used to obtain more precise asymptotic formulae for eigenvalues and norming constants of this problem.
math.SP↗