English

A Gelfand-Levitan trace formula for generic quantum graphs

Mathematical Physics 2022-03-02 v2 math.MP Spectral Theory Quantum Physics

Abstract

We formulate and prove a Gelfand-Levitan trace formula for general quantum graphs with arbitrary edge lengths and coupling conditions which cover all self-adjoint operators on quantum graphs, except for a set of measure zero. The formula is reminiscent of the original Gelfand-Levitan result on the segment with Neumann boundary conditions.

Keywords

Cite

@article{arxiv.1901.07790,
  title  = {A Gelfand-Levitan trace formula for generic quantum graphs},
  author = {Pedro Freitas and Jiri Lipovsky},
  journal= {arXiv preprint arXiv:1901.07790},
  year   = {2022}
}

Comments

16 pages. This is a preprint of an article published in Anal. Math. Phys. The final authenticated version is available online at: https://doi.org/10.1007/s13324-021-00487-3

R2 v1 2026-06-23T07:19:31.655Z