A practical method for recovering Sturm–Liouville problems from the Weyl function

نویسندگان

چکیده

In the paper we propose a direct method for recovering Sturm–Liouville potential from Weyl–Titchmarsh m-function given on countable set of points. We show that using Fourier–Legendre series expansion transmutation operator integral kernel problem reduces to an infinite linear system equations, which is uniquely solvable if so original problem. The solution this allows one reconstruct characteristic determinant and hence obtain eigenvalues as its zeros compute corresponding norming constants. As result, inverse transformed with spectral density function, Kravchenko Torba (2021 Inverse Problems 37 015015) applied. proposed leads efficient numerical algorithm solving variety problems. particular, problems in two spectra or some parts three more are given, depend variable boundary parameter (including dependent conditions), partially known partial quantum graphs.

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ژورنال

عنوان ژورنال: Inverse Problems

سال: 2021

ISSN: ['0266-5611', '1361-6420']

DOI: https://doi.org/10.1088/1361-6420/abff06