Inversion of trace formulas for a Sturm-Liouville operator

06/28/2019

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by   Xiang Xu, et al.

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This paper revisits the classical problem "Can we hear the density of a string?", which can be formulated as an inverse spectral problem for a Sturm-Liouville operator. Based on inverting a sequence of trace formulas, we propose a new numerical scheme to reconstruct the density. Numerical experiments are presented to verify the validity and effectiveness of the numerical scheme.