Krein-Feller算子关于$\boldsymbol V$ -变量Cantor测度的谱渐近性
Spectral Asymptotics for Krein-Feller-Operators with respect to $\boldsymbol V$-Variable Cantor Measures
摘要：
研究了广义二阶微分算子$\frac{d}{d μ} \frac{d}{d x}$的Dirichlet和Neumann特征值计数函数的极限行为，其中$μ$是某个紧区间$[a,b]$上的有限无原子Borel测度.因此，我们首先回顾了迄今为止得到的关于这些算子谱渐近性的结果。然后，我们对所谓的随机$V$ -变量Cantor测度的收敛性给出了一个命题.
英文摘要：
We study the limiting behavior of the Dirichlet and Neumann eigenvalue counting function of generalized second order differential operators $\frac{d}{d μ} \frac{d}{d x}$, where $μ$ is a finite atomless Borel measure on some compact interval $[a,b]$. Therefore, we firstly recall the results of the spectral asymptotics for these operators received so far. Afterwards, we make a proposition about the convergence behavior for so called random $V$-variable Cantor measures.
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