On the finiteness of logarithmic Hamiltonians for Volterra-type lattices in terms of the spectral measures of Jacobi operators

Andrey Osipov

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arXiv · 2509.26250

On the finiteness of logarithmic Hamiltonians for Volterra-type lattices in terms of the spectral measures of Jacobi operators

Andrey Osipov

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Abstract

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. 2025-09-30. On the finiteness of logarithmic Hamiltonians for Volterra-type lattices in terms of the spectral measures of Jacobi operators. https://arxiv.org/abs/2509.26250

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