A spectral Szego theorem on the real line
R. V. Bessonov, S. A. Denisov

TL;DR
This paper characterizes measures on the real line with finite entropy integral using inverse spectral theory and provides criteria for spectral measures of Krein strings to have converging logarithmic integrals.
Contribution
It introduces a spectral Szego theorem on the real line linking measures with finite entropy to Hamiltonians in inverse spectral theory.
Findings
Characterization of measures with finite entropy integral
Criterion for spectral measures of Krein strings
Connection between spectral measures and Hamiltonians
Abstract
We characterize even measures on the real line with finite entropy integral in terms of Hamiltonian generated by 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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