Inverse problems for Sturm-Liouville operators on a star-shaped graph with mixed spectral data

The partial inverse spectral problem for Sturm-Liouville operators on a star-shaped graph was studied. The authors showed that if the potentials but one were known a priori, then the unknown potential on the whole interval can be uniquely determined by part of information of the potential and part o...

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Bibliographic Details
Published in:Applicable analysis 2020-10, Vol.99 (14), p.2371-2380
Main Authors: Wang, Yu Ping, Shieh, Chung-Tsun
Format: Article
Language:English
Subjects:
differential operator on graphs
Eigenvalues
Entire functions
inverse problem
Inverse problems
mixed spectral data
Operators (mathematics)
Sturm-Liouville operator
Weyl function
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Summary:The partial inverse spectral problem for Sturm-Liouville operators on a star-shaped graph was studied. The authors showed that if the potentials but one were known a priori, then the unknown potential on the whole interval can be uniquely determined by part of information of the potential and part of eigenvalues. The methods employed rest on the Weyl's m-function and theory concerning densities of zeros of entire functions.
ISSN:0003-6811
1563-504X
DOI:10.1080/00036811.2019.1566527