Understanding Quantum Graphs
P. Kurasov
Dept. of Mathematics, Stockholm Univ., 106 91 Stockholm, Sweden
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Current understanding of spectral asymptotics for quantum graphs is described. It is discussed how these results can be applied to inverse problems. In particular it is analysed whether the inverse spectral problem has a unique solution in the spirit of classical Ambartsumian theorem: a complete overview is provided.

DOI:10.12693/APhysPolA.136.797
topics: quantum graphs, spectral asymptotics, isospectrality