Generating functions of cauchystieltjes type for orthogonal polynomials

Marek Boejko; Nizer Demni

doi:10.1142/S0219025709003586

Generating functions of cauchystieltjes type for orthogonal polynomials

Marek Boejko, Nizer Demni

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We give a free probabilistic interpretation of the multiplicative renormalization method. As a byproduct, we give a short proof of the AsaiKuboKuo problem on the characterization of the family of measures for which this method applies with h(x) = (1 - x)^-1 which turns out to be the free Meixner family. We also give a representation of the Voiculescu transform of all free Meixner laws (even in the non-freely infinitely divisible case).

Original language	English (US)
Pages (from-to)	91-98
Number of pages	8
Journal	Infinite Dimensional Analysis, Quantum Probability and Related Topics
Volume	12
Issue number	1
DOIs	https://doi.org/10.1142/S0219025709003586
State	Published - Mar 2009

Keywords

Continued fractions
Free Meixner laws
Generating function
Jacobi-Szegö parameters
Multiplicative renormalization

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Statistics and Probability
Mathematical Physics
Applied Mathematics

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10.1142/S0219025709003586

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AB - We give a free probabilistic interpretation of the multiplicative renormalization method. As a byproduct, we give a short proof of the AsaiKuboKuo problem on the characterization of the family of measures for which this method applies with h(x) = (1 - x)-1 which turns out to be the free Meixner family. We also give a representation of the Voiculescu transform of all free Meixner laws (even in the non-freely infinitely divisible case).

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KW - Free Meixner laws

KW - Generating function

KW - Jacobi-Szegö parameters

KW - Multiplicative renormalization

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Generating functions of cauchystieltjes type for orthogonal polynomials

Abstract

Keywords

ASJC Scopus subject areas

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