Uniform stability of the inverse Sturm-Liouville problem on a star-shaped graph
E.E. Chitorkin, N.P. Bondarenko
TL;DR
This paper investigates the inverse spectral problem for Sturm-Liouville operators on star-shaped graphs, demonstrating the uniform stability of potential recovery from spectral data across the entire graph.
Contribution
It establishes the uniform stability of inverse spectral problems for Sturm-Liouville operators on star-shaped graphs, a novel result in spectral graph theory.
Findings
Proved uniform stability of inverse spectral problems on star-shaped graphs
Demonstrated potential recovery from spectral data is stable across the entire graph
Extended inverse spectral theory to complex graph structures
Abstract
In this paper, we study the inverse spectral problem for the Sturm-Liouville operators on a star-shaped graph, which consists in the recovery of the potentials from specral data or several spectra. The uniform stability of these inverse problems on the whole graph is proved.
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Taxonomy
TopicsSpectral Theory in Mathematical Physics · Numerical methods in inverse problems · Mathematical Analysis and Transform Methods