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.
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}
}