On a generalization of the three spectral inverse problem

O. P. Boyko; O. M. Martynyuk; V. N. Pivovarchik

On a generalization of the three spectral inverse problem

Spectral Theory 2016-09-13 v1 Classical Analysis and ODEs

Authors: O. P. Boyko , O. M. Martynyuk , V. N. Pivovarchik

Abstract

We consider a generalization of the three spectral inverse problem, that is, for given spectrum of the Dirichlet-Dirichlet problem (the Sturm-Liouville problem with Dirichlet conditions at both ends) on the whole interval $[0,a]$ , parts of spectra of the Dirichlet-Neumann and Dirichlet-Dirichlet problems on $[0,a/2]$ and parts of spectra of the Dirichlet-Newman and Dirichlet-Dirichlet problems on $[a/2,a]$ , we find the potential of the Sturm-Liouville equation.

Keywords

inverse spectral problem Sturm-Liouville equation Dirichlet-Dirichlet problem Dirichlet-Neumann problem potential reconstruction

Cite

@article{arxiv.1609.02955,
  title  = {On a generalization of the three spectral inverse problem},
  author = {O. P. Boyko and O. M. Martynyuk and V. N. Pivovarchik},
  journal= {arXiv preprint arXiv:1609.02955},
  year   = {2016}
}

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Published in Methods of Functional Analysis and Topology (MFAT), available at http://mfat.imath.kiev.ua/article/?id=842

On a generalization of the three spectral inverse problem

Abstract

Keywords

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