Continuity of spectral averaging

Abstract

We consider averages $\kappa$ of spectral measures of rank one perturbations with respect to a $\sigma$-finite measure $\nu$. It is examined how various degrees of continuity of $\nu$ with respect to $\alpha$-dimensional Hausdorff measures ($0\le \alpha \le 1$) are inherited by $\kappa$. This extends Kotani's trick where $\nu$ is simply the Lebesgue measure.

References in corpus (1)

• Spectral averaging techniques for Jacobi matrices