About one inverse problem for the Sturm-Liouville operator
Functional Analysis
2019-12-30 v5 Spectral Theory
Abstract
We consider the spectral problems for the Sturm-Liouville operator generated by the Dirichlet, Neumann, Dirichlet-Neumann and Neumann-Dirichlet conditions. The necessary and sufficient condition for the coincidence of the spectrum of the Dirichlet-Neumann and Neumann-Dirichlet problems is proved. Also the necessary and sufficient condition for the coincidence of the spectrum, except zero, of the Dirichlet and Neumann problems is proved. An application to periodic and anti-periodic problems is given.
Keywords
Cite
@article{arxiv.1912.03129,
title = {About one inverse problem for the Sturm-Liouville operator},
author = {B. N. Biyarov},
journal= {arXiv preprint arXiv:1912.03129},
year = {2019}
}
Comments
16 pages