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The fixed point for a transformation of Hausdorff moment sequences and iteration of a rational function. (English) Zbl 1162.44004

Hausdorff moment sequences are of the form \[ \int^1_0t^nd\mu (t),\quad (n\geq 0) \] where \(\mu\) is positive measure on \([0,1]\). Stieltjes moment sequences are of the form \[ \int^\infty_0t^nd\mu(t), \quad (n\geq 0) \] where \(\mu\) is positive measure on \([0,\infty)\).
In earlier papers these authors have introduced a nonlinear multiplicative transformation from the class of Hausdorff moment sequences to the class of Stieltjes moment sequences and a nonlinear transformation on the set of Hausdorff moment sequences into intself. In this paper the authors study the properties of fixed points of these transformations and determine the associated probability measure \(\mu\), called the fixed point measure.

MSC:

44A60 Moment problems
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