Inverse spectral problems for Dirac operators on a star graph with mixed boundary conditions

This paper is devoted to some inverse spectral problems for Dirac operators on a star graph with mixed boundary conditions in boundary vertices. By making use of Rouché's theorem, we derive the eigenvalue asymptotics of these operators. Besides, we show that for each of these operators, if the...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2021-09, Vol.44 (13), p.10663-10672
Main Authors: Liu, Dai‐Quan, Yang, Chuan‐Fu
Format: Article
Language:English
Subjects:
Apexes
Boundary conditions
Dirac operator
Eigenvalues
Graph theory
inverse spectral problem
mixed boundary conditions
Operators
star graph
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Summary:This paper is devoted to some inverse spectral problems for Dirac operators on a star graph with mixed boundary conditions in boundary vertices. By making use of Rouché's theorem, we derive the eigenvalue asymptotics of these operators. Besides, we show that for each of these operators, if the potentials are known a priori for all but one edge on the graph, then the potential on the remaining edge is uniquely determined by part of the potential on this edge and part of its spectrum. Our method relies upon some estimates of infinite products given by Horváth.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.7436