A Gelfand-Levitan trace formula for generic quantum graphs

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.

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

References in corpus (3)

• Quantum graphs: an introduction and a brief survey
• The trace formula for quantum graphs with general self adjoint boundary conditions
• Resonances from perturbations of quantum graphs with rationally related edges