论文标题
在Sturm-Liouville问题的范围内，算术上有相似的重量
On the spectrum of the Sturm-Liouville problem with arithmetically self-similar weight
论文作者
论文摘要
考虑到Sturm-liouville问题的光谱渐近性与算术相似的奇异重量。 A. A. Vladimirov和I. A. Sheipak以及作者的先前结果依赖于光谱周期性属性，这对重量的自相似性参数施加了重大限制。这项工作介绍了一种估计特征值计数函数的新方法。这允许考虑更广泛的自相似措施。获得的渐近物应用于绿色高斯过程的小球偏差问题。
Spectral asymptotics of the Sturm-Liouville problem with an arithmetically self-similar singular weight is considered. Previous results by A. A. Vladimirov and I. A. Sheipak, and also by the author, rely on the spectral periodicity property, which imposes significant restrictions on the self-similarity parameters of the weight. This work introduces a new method to estimate the eigenvalue counting function. This allows to consider a much wider class of self-similar measures. The obtained asymptotics is applied to the small ball deviations problem for the Green Gaussian processes.
