Abstract
We characterize even measures μ=wdx+μs on the real line R with finite entropy integral ∫Rlogw(t)1+t2dt>−∞ in terms of 2×2 Hamiltonians generated by μ in the sense of the inverse spectral theory. As a corollary, we obtain criterion for spectral measure of Krein string to have converging logarithmic integral.
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