# Eigenvalue Approximation for Krein-Feller-Operators

## TL;DR

This paper investigates how the eigenvalues and eigenfunctions of Krein-Feller-Operators behave as the underlying probability measures converge, providing explicit representations and convergence rates, especially on the Cantor set.

## Contribution

It introduces a measure-theoretic sine function representation of eigenvalues and analyzes their limiting behavior and convergence speed for sequences approaching invariant measures.

## Key findings

- Eigenvalues are zeros of measure-theoretic sine functions.
- Eigenfunctions' limiting behavior is characterized.
- Convergence rates of eigenvalues and eigenfunctions are established.

## Abstract

We study the limiting behavior of the eigenvalues of Krein-Feller-Operators with respect to weakly convergent probability measures. Therefore, we give a representation of the eigenvalues as zeros of measure theoretic sine functions. Further, we make a proposition about the limiting behavior of the previously determined eigenfunctions. With the main results we finally determine the speed of convergence of eigenvalues and -functions for sequences which converge to invariant measures on the Cantor set.