The study establishes correspondences between finite logarithmic Hamiltonians in Volterra lattices, suggesting implications for Jacobi operator theory.
We establish a correspondence between the semi-infinite and infinite Volterra lattices having a finite logarithmic Hamiltonian and certain classes of even probability measures. In doing so, we apply the inverse spectral theory of Jacobi operators and the theory of orthogonal polynomials. A similar correspondence is established for semi-infinite modified Volterra lattices.
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Andrey Osipov (2025) studied this question.
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