Pedro Freitas, Jiri Lipovsky
A Gelfand-Levitan trace formula for generic quantum graphs
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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.