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arXiv · 1711.05671

A spectral Szego theorem on the real line

R. V. Bessonov·S. A. Denisov
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Abstract

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 by $\mu$ in the sense of inverse spectral theory. As a corollary, we obtain criterion for spectral measure of Krein string to have converging logarithmic integral.

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R. V. Bessonov, S. A. Denisov. 2017-11-15. A spectral Szego theorem on the real line. https://doi.org/10.1016/j.aim.2019.106851

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