Title: On Reconstruction of the Potential in the Sturm-Liouville Equation from Incomplete Spectral Data
Abstract: During past few years methods were developed to reconstruct negative potentials in the Sturm-Liouville equation through characteristics of a discrete spectrum. Several numerical tests clarify limitations of these methods. The tests show: (1) only the negative part of a potential having negative and positive parts can be reconstructed through characteristics of the negative spectrum of the Sturm-Liouville equation (the potential is multiplied by a suitable factor ω); (2) spectral data for eigenvalues not larger than –Bω 2, B>0, can be used to reconstruct the potential where it is less than –Bω 2; (3) discontinuities of the potential result in deterioration of approximations with the growth of ω.
Publication Year: 2013
Publication Date: 2013-03-15
Language: en
Type: book-chapter
Indexed In: ['crossref']
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