Reflectionless measures with a point mass and singular continuous component

Details Reflectionless measures with a point mass and singular continuous component Reflectionless measures with a point mass and singular continuous component

2007-11-06

arxiv.org/abs/0711.0948v1

Physics

Mathematical Physics

Scientific paper

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).

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