We investigate absolutely continuous spectrum of generalized indefinite strings. By following an approach of Deift and Killip, we establish stability of the absolutely continuous spectra of two model examples of generalized indefinite strings under rather wide perturbations. In particular, one of these results allows us to prove that the absolutely continuous spectrum of the isospectral problem associated with the conservative Camassa–Holm flow in the dispersive regime is essentially supported on the interval \([1/4,\infty )\).

中文翻译：

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关于广义不定串的绝对连续谱

我们研究了广义不定串的绝对连续谱。通过遵循 Deift 和 Killip 的方法，我们建立了广义不定弦的两个模型示例在相当宽的扰动下的绝对连续谱的稳定性。特别是，这些结果之一使我们能够证明与离散区域中保守的 Camassa-Holm 流相关的等谱问题的绝对连续谱基本上在区间\([1/4,\infty )\)上得到支持.