Continuity of spectral averaging

Details Continuity of spectral averaging Continuity of spectral averaging

2010-09-20

arxiv.org/abs/1009.3694v1

Proc. Math. Soc., posted on August 20, 2010, PII S 0002-9939(2010)10629-9

Physics

Mathematical Physics

Scientific paper

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 ($0 \leq \alpha \leq 1$) are inherited by $\kappa$. This extends
Kotani's trick where $\nu$ is simply the Lebesgue measure.

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