Abstract The theory of almost periodic functions is used to investigate spectral properties of Schrodinger operators on metric graphs, also known as quantum graphs. In particular we prove that two Schrodinger operators may have asymptotically close spectra if and only if the corresponding reference Laplacians are isospectral. Our result implies that a Schrodinger operator is isospectral to the standard Laplacian on a may be different metric graph only if the potential is identically equal to zero.

中文翻译：

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渐近等谱量子图和广义三角多项式

摘要 几乎周期函数理论用于研究度量图（也称为量子图）上薛定谔算符的谱性质。特别地，我们证明了当且仅当相应的参考拉普拉斯算子是等谱的时，两个薛定谔算子可能具有渐近接近的谱。我们的结果意味着薛定谔算子与标准拉普拉斯算子在一个可能不同的度量图上是等谱的，只有当势完全等于零时。