Spectral characterization of measures on the real line with ..finite logarithmic integral

We consider even measures on the real line and de Branges canonical systems generated by them. Then, we give a criterion for the logarithmic integral to converge in terms of coefficients of the Hamiltonian. This complements the celebrated Krein-Wiener theorem and generalizes the Szego theorem for measures on the unit circle. Some connections to prediction problem for Gaussian stationary processes will be discussed (based on joint work with R. Bessonov).