Markov–Krein transform
Volume 144 / 2016
Colloquium Mathematicum 144 (2016), 137-156
MSC: Primary 44A60; Secondary 60B10, 60E10, 65D07.
DOI: 10.4064/cm6235-10-2015
Published online: 9 March 2016
Abstract
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.
