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Recovering the shape of a quantum caterpillar tree by two spectra

Mathematical Physics 2023-03-30 v2 math.MP

Abstract

We show how to find the shape of an equilateral caterpillar tree using the spectra of the Neumann and the Dirichlet problems generated by the Sturm-Liouville equation on this tree. We prove that in the case of a caterpillar tree the spectra of the Neumann and Dirichlet problems uniquely determine the shape of the tree.

Keywords

Cite

@article{arxiv.2303.14670,
  title  = {Recovering the shape of a quantum caterpillar tree by two spectra},
  author = {Dmytro Kaliuzhnyi-Verbovetskyi and Vyacheslav Pivovarchik},
  journal= {arXiv preprint arXiv:2303.14670},
  year   = {2023}
}

Comments

9 pages, 1 figure. arXiv admin note: substantial text overlap with arXiv:2301.05939