KdV ’95 pp 435-443 | Cite as

Moment Problem of Hamburger, Hierarchies of Integrable Systems, and the Positivity of Tau-Functions

  • Yoshimasa Nakamura
  • Yuji Kodama


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.

Key words

Hamburger moment problem Moser’s system Kac-van Moerbeke system tau functions 


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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Yoshimasa Nakamura
    • 1
  • Yuji Kodama
    • 2
  1. 1.Applied Mathematics LaboratoryDoshisha UniversityTanabe, KyotoJapan
  2. 2.Department of MathematicsThe Ohio State UniversityColumbusUSA

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