Abstract
A moment problem of Hamburger is studied to find a parametric Stieltjes measure from given moments. It is shown that if a deformation, or a dynamics, of moments is governed by a hierarchy of a Kac-van Moerbeke system, then the Stieltjes measure can be constructed explicitly by integrating a hierarchy of Moser's nonlinear dynamical system. The positivity of tau-functions is related to the existence of the Stieltjes measure at a deep level.
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Nakamura, Y., Kodama, Y. Moment problem of Hamburger, hierarchies of integrable systems, and the positivity of tau-functions. Acta Appl Math 39, 435–443 (1995). https://doi.org/10.1007/BF00994647
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DOI: https://doi.org/10.1007/BF00994647