Inverse Sturm-Liouville problems: some recent developments

Abstract

We consider numerical methods for obtaining, from spectral data, information on the potentials of Sturm--Liouville operators. In particular, we describe some recent work on methods using an asymptotic correction technique of Paine, de Hoog and Anderssen. Topics covered include a discussion of difficulties arising from the scarcity of accurate data in physical applications, a preview of some work in progress on the Hochstadt--Lieberman problem, and suggestions for future work. References

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