Analyticity and uniform stability of the inverse singular Sturm--Liouville spectral problem

TL;DR

This paper establishes that the potential in a Sturm--Liouville problem depends analytically and Lipschitz continuously on spectral data, for operators with distributional potentials in a Sobolev class, enhancing understanding of inverse spectral problems.

Contribution

It proves the analyticity and Lipschitz continuity of the potential's dependence on spectral data for a broad class of Sturm--Liouville operators with distributional potentials.

Findings

Potential depends analytically on spectral data

Dependence is Lipschitz continuous

Results apply to operators with distributional potentials in Sobolev spaces

Abstract

We prove that the potential of a Sturm--Liouville operator depends analytically and Lipschitz continuously on the spectral data (two spectra or one spectrum and the corresponding norming constants). We treat the class of operators with real-valued distributional potentials in the Sobolev class W^{s-1}_2(0,1), s\in[0,1].