Abstract This article is concerned with the isospectral problem − f ″ + 1 4 f = z ω f + z 2 υ f for the periodic conservative Camassa–Holm flow, where ω is a periodic real distribution in H loc − 1 ( R ) and υ is a periodic non-negative Borel measure on R . We develop basic Floquet theory for this problem, derive trace formulas for the associated spectra and establish continuous dependence of these spectra on the coefficients with respect to a weak⁎ topology.

中文翻译：

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周期性保守 Camassa-Holm 流的迹公式和谱的连续相关性

摘要 本文关注周期性保守 Camassa-Holm 流的等谱问题 − f ″ + 1 4 f = z ω f + z 2 υ f，其中 ω 是 H loc − 1 ( R ) 中的周期性实分布υ 是 R 上的周期性非负 Borel 测度。我们为这个问题开发了基本的 Floquet 理论，推导出相关谱的迹公式，并建立这些谱对弱拓扑系数的连续依赖性。