Abstract:The oscillation equation for a singular string with discrete weight generated by a self-similar $n$-link multiplier in the Sobolev space with a negative smoothness index is considered. It is shown that in the case of a noncompact multiplier, the string problem is equivalent to the spectral problem for an $(n-1)$-periodic Jacobi matrix. In the case of $n=3$, a complete description of the spectrum of the problem is given, and a criterion for emergence of an eigenvalue in a gap of the continuous spectrum is obtained.

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中文翻译：

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权重为非紧乘子的加权字符串方程：连续谱和特征值

摘要:考虑了Sobolev空间中具有负平滑指数的自相似$n$-link乘子生成的具有离散权重的奇异弦的振荡方程。结果表明，在非紧乘子的情况下，字符串问题等价于 $(n-1)$-周期 Jacobi 矩阵的谱问题。在$n=3$的情况下，给出了问题谱的完整描述，得到了连续谱间隙中特征值出现的判据。

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