Partial Inverse Problems for Dirac Operators on Star Graphs

Abstract

Partial inverse problems for Dirac operators on star graphs are studied. We consider Dirac operators on the graphs, and prove that the potential on one edge is uniquely determined by part of its spectra and part of the potential provided that the potentials on the remaining edges are given a priori. This extends the results of Horváth to Dirac operators on the graphs.

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Acknowledgements

The authors wish to express their sincere appreciation to the anonymous reviewers for their careful work and thoughtful suggestions that have helped improve this paper substantially. In addition, the research work was supported by the National Natural Science Foundation of China (11871031 and 11611530682).

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Correspondence to Dai-Quan Liu.

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Liu, DQ., Yang, CF. Partial Inverse Problems for Dirac Operators on Star Graphs. Mediterr. J. Math. 17, 180 (2020). https://doi.org/10.1007/s00009-020-01620-5

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Keywords

  • Partial inverse problem
  • Star graph
  • Dirac operator
  • Horváth-type theorem

Mathematics Subject Classification

  • 34A55
  • 34B45
  • 34L40
  • 47E05