Geodesic
Markov–Krein transform
Jacques Faraut 1   ; Faiza Fourati 2
1 Institut de Mathématiques de Jussieu Université Pierre et Marie Curie 4 place Jussieu, case 247 75252 Paris Cedex 05, France
2 Institut Préparatoire aux études d’Ingénieurs de Tunis Université de Tunis 1089 Montfleury, Tunis, Tunisie
Colloquium Mathematicum, Tome 144 (2016) no. 1, pp. 137-156 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/cm6235-10-2015
Mots-clés : markov krein transform maps positive measure real line probability measure implicitly defined through identity linking holomorphic functions paper explicit formula given its proof obtained considering boundary values holomorhic functions transform appears several classical questions analysis probability theory markov moment problem dirichlet distributions processes orbital measures asymptotic property transform involves thorin bondesson distributions

Jacques Faraut  1   ; Faiza Fourati  2

1 Institut de Mathématiques de Jussieu Université Pierre et Marie Curie 4 place Jussieu, case 247 75252 Paris Cedex 05, France
2 Institut Préparatoire aux études d’Ingénieurs de Tunis Université de Tunis 1089 Montfleury, Tunis, Tunisie 
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Jacques Faraut; Faiza Fourati. Markov–Krein transform. Colloquium Mathematicum, Tome 144 (2016) no. 1, pp. 137-156. doi: 10.4064/cm6235-10-2015

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