English

Uniform stability for the Hochstadt-Lieberman problem

Spectral Theory 2024-10-15 v1

Abstract

In this paper, we prove the uniform stability of the Hochstadt-Lieberman problem, which consists in the recovery of the Sturm-Liouville potential on a half-interval from the spectrum and the known potential on the other half-interval. For this purpose, we reduce the half-inverse problem to the complete one for the unknown potential. Our method relies on the uniform stability for the direct and inverse Sturm-Liouville problems, for recovering sine-type functions from their zeros, and the uniform boundedness of Riesz bases of sines and cosines.

Keywords

Cite

@article{arxiv.2410.10326,
  title  = {Uniform stability for the Hochstadt-Lieberman problem},
  author = {Natalia P. Bondarenko},
  journal= {arXiv preprint arXiv:2410.10326},
  year   = {2024}
}
R2 v1 2026-06-28T19:20:18.660Z