Markov-Krein transform (Q2804283)

An implicit definition of the Markov-Krein transform of a bounded positive measure \(\nu\) on the real line into a probability measure \(\mu\) is given by the relation \(\int_{\mathbb R}(z-t)^{-\kappa}\mu(dt)=\exp(\int_{\mathbb R}\log(z-u) \nu(du))\), where \(\kappa=\nu(\mathbb R)\). The aim of this paper is to give an explicit formula for the Markov-Krein transform, via the boundary values of holomorphis functions. The authors note that ``this formula is essentially a special case of one obtained'' by \textit{D. M. Cifarelli} and \textit{E. Regazzini} [Ann. Stat. 18, No. 1, 429--442 (1990; Zbl 0706.62012)].