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.
Mathematics Subject Classifications (1991): Primary 58F07; Secondary 34A05.
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Nakamura, Y., Kodama, Y. (1995). Moment Problem of Hamburger, Hierarchies of Integrable Systems, and the Positivity of Tau-Functions. In: Hazewinkel, M., Capel, H.W., de Jager, E.M. (eds) KdV ’95. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0017-5_24
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DOI: https://doi.org/10.1007/978-94-011-0017-5_24
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