Spectral Asymptotics for Krein-Feller-Operators with respect to $\boldsymbol V$-Variable Cantor Measures

Abstract

We study the limiting behavior of the Dirichlet and Neumann eigenvalue counting function of generalized second order differential operators $\frac{d}{d \mu} \frac{d}{d x}$, where $\mu$ 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.