In this research, I derive a refined asymptotic expression for the eigenvalues, lnn ∈Z , of the operator matrix from the telegrapher's equation to accuracy O(1/n²). First, the expression for the "shooting function" is refined to O(1/n²) using a "fake potential" and a Neumann series. Then, this expression for the "shooting function" is used to refine the expressions for the eigenvalues. This refinement of the previously published results of accuracy O(1/| n|) enables the inverse spectral problem (recovering unknown resistance) to be solved in numerical experiments, using Fourier series. One application of this recovery process would be to find a fault in the insulation of a submarine telegraph cable without having to physically inspect every inch of the cable.
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机译：在这项研究中，我从电报员的方程式到精度O（1 /n²），推导了算子矩阵特征值lnn∈Z的精细渐近表达式。首先，使用“假电位”和诺伊曼级数将“射击函数”的表达式精炼为O（1 /n²）。然后，用于“拍摄功能”的该表达式用于细化特征值的表达式。对精度为O（1 / | n |）的先前发表的结果的这种改进使使用傅立叶级数的反谱问题（恢复未知电阻）能够在数值实验中得以解决。此恢复过程的一种应用是找到海底电报电缆绝缘层中的故障，而无需实际检查电缆的每一英寸。
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