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