On the constructive solution of an inverse Sturm-Liouville problem

Abstract

The necessary and sufficient conditions are found for the two sequences ${\left\{{\mu }_n\right\}}_{n=0}^{\infty }$ and ${\left\{a_n\right\}}_{n=0}^{\infty }$ to be the spectrum and the norming constants respectively, for a boundary value problem $-y^{\prime \prime }+q\left(x\right)y=\mu y,$ $y\left(0\right)=0,$ $y\left(\pi \right)\cos \beta +y^{\prime }\left(\pi \right)\sin \beta =0,$ $\beta \in \left(0,\pi \right),$ with $q\in L_{\mathbb{R}}^1\left[0,\pi \right].$

35 pages