Markov–Krein transform

Volume 144 / 2016

Jacques Faraut, Faiza Fourati Colloquium Mathematicum 144 (2016), 137-156 MSC: Primary 44A60; Secondary 60B10, 60E10, 65D07. DOI: 10.4064/cm6235-10-2015 Published online: 9 March 2016


The Markov–Krein transform maps a positive measure on the real line to a probability measure. It is implicitly defined through an identity linking two holomorphic functions. In this paper an explicit formula is given. Its proof is obtained by considering boundary values of holomorhic functions. This transform appears in several classical questions in analysis and probability theory: Markov moment problem, Dirichlet distributions and processes, orbital measures. An asymptotic property for this transform involves Thorin–Bondesson distributions.


  • Jacques FarautInstitut de Mathématiques de Jussieu
    Université Pierre et Marie Curie
    4 place Jussieu, case 247
    75252 Paris Cedex 05, France
  • Faiza FouratiInstitut Préparatoire
    aux études d’Ingénieurs de Tunis
    Université de Tunis
    1089 Montfleury, Tunis, Tunisie

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