Under study is the spectral asymptotics of the Sturm–Liouville problem with a singular self-conformal weight measure. We assume that the conformal iterated function system generating the weight measure satisfies a stronger version of the bounded distortion property. The power exponent of the main term of the eigenvalue counting function asymptotics is obtained under the assumption. This generalizes the result by Fujita in the case of self-similar (self-affine) measures.

中文翻译：

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具有自共形奇异权重的 Sturm-Liouville 问题的谱渐近性

正在研究的是 Sturm-Liouville 问题的谱渐近性，该问题具有奇异的自保形权重度量。我们假设生成权重度量的保形迭代函数系统满足有界失真属性的更强版本。假设得到特征值计数函数渐近的主项的幂指数。这概括了 Fujita 在自相似（自仿射）测度的情况下的结果。