A spectral Szego theorem on the real line

R. V. Bessonov, S. A. Denisov

We characterize even measures $\mu =wdx+{\mu }_s$ on the real line with finite entropy integral ${\int }_R\frac{\log w(t)}{1+t^2}dt>-\infty$ in terms of $2\times 2$ Hamiltonian generated b…