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Markov-Krein transform

Jacques Faraut, Faiza Fourati (2016)

Colloquium Mathematicae

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...

Moment sequences and abstract Cauchy problems

Claus Müller (2003)

Commentationes Mathematicae Universitatis Carolinae

We give a new characterization of the solvability of an abstract Cauchy problems in terms of moment sequences, using the resolvent operator at only one point.

Moments of vector measures and Pettis integrable functions

Miloslav Duchoň (2011)

Czechoslovak Mathematical Journal

Conditions, under which the elements of a locally convex vector space are the moments of a regular vector-valued measure and of a Pettis integrable function, both with values in a locally convex vector space, are investigated.

Multivariate moment problems : geometry and indeterminateness

Mihai Putinar, Claus Scheiderer (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

The most accurate determinateness criteria for the multivariate moment problem require the density of polynomials in a weighted Lebesgue space of a generic representing measure. We propose a relaxation of such a criterion to the approximation of a single function, and based on this condition we analyze the impact of the geometry of the support on the uniqueness of the representing measure. In particular we show that a multivariate moment sequence is determinate if its support has dimension one and...

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