On the constructive solution of an inverse Sturm-Liouville problem

Avetik Pahlevanyan

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arXiv · 1608.01459

On the constructive solution of an inverse Sturm-Liouville problem

Avetik Pahlevanyan

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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 $-y'' + q \left( x \right) y = \mu y,$ $y \left(0\right)=0,$ $y\left( \pi \right)\cos \beta + y'\left( \pi \right)\sin \beta = 0,$ $\beta \in \left( 0, \pi \right),$ with $q \in L_{\mathbb{R}}^1 \left[0, \pi \right].$

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BibTeX RIS

Avetik Pahlevanyan. 2016-08-04. On the constructive solution of an inverse Sturm-Liouville problem. https://arxiv.org/abs/1608.01459

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