Szegö measures and vibration of Krein strings

We give a dynamical characterization of Szegö measures on the real line. Szegö condition for a measure $\mu=w\,dx+\mu_s$,
$$\int_{\mathbb{R}}\frac{\log w(x)}{1 + x^2}\,dx > -\infty,$$
is proved to be equivalent to a stable propagation of waves on an associated Krein string. Related results in scattering theory of Dirac operators will be also discussed. Joint work with Sergey Denisov (University of Wisconsin-Madison).
The author is supported by the Russian Science Foundation grant 19-71-30002.