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.

中文翻译：

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通用量子图的Gelfand-Levitan跟踪公式

我们为具有任意边长和耦合条件的一般量子图制定并证明了Gelfand-Levitan迹线公式，该条件涵盖了量子图上所有自伴算子，但测度为零。该公式让人想起带有Neumann边界条件的线段上原始Gelfand-Levitan结果。