Reflectionless measures with a point mass and singular continuous component
Mathematical Physics
2007-11-07 v1 Complex Variables
math.MP
Abstract
We construct mesures supported on a compact subset E of the real line having zero principal value of their Cauchy integral a.e. on E with respect to Lebesgue measure and having singular components. E is sufficiently regular (Widom property is satisfied) but not homogeneous as for homogeneous spectrum such construction is impossible. This impossibility played an important role in characterizing almost periodic Jacobi matrices with homogeneous spectrum (Sodin-Yuditskii).
Cite
@article{arxiv.0711.0948,
title = {Reflectionless measures with a point mass and singular continuous component},
author = {F. Nazarov and A. Volberg and P. Yuditskii},
journal= {arXiv preprint arXiv:0711.0948},
year = {2007}
}