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

Abstract

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.

Keywords:

• inverse problem
• differential operator on graphs
• Sturm–Liouville operator
• Weyl function
• mixed spectral data

2010 Mathematics Subject Classifications:

• 34A55
• 34B09
• 34B45
• 47E05

Acknowledgements

The authors would like to thank the anonymous referees for valuable suggestions, which helped to improve the readability and quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.