Generating functions of Cauchy-Stieltjes type for orthogonal polynomials
Marek Bozejko, Nizar Demni
TL;DR
This paper uses free probability to characterize measures suitable for a specific multiplicative renormalization method, providing a formula for their Voiculescu Transforms, advancing understanding of orthogonal polynomials.
Contribution
It introduces a free probability framework to characterize measures related to Cauchy-Stieltjes type generating functions for orthogonal polynomials, with a new representation formula.
Findings
Characterization of measures via free probability
Representation formula for Voiculescu Transforms
Application to orthogonal polynomial generating functions
Abstract
We characterize by the use of free probability the family of measures for which the mulitiplicative renormalization method applies with h(x) = (1-x)^_{-1}. This provides a representation formula for their Voiculescu Transforms.
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Taxonomy
TopicsMathematical functions and polynomials · Iterative Methods for Nonlinear Equations · Matrix Theory and Algorithms