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Contents of PMS, Vol. 21, Fasc. 1,
pages 159 - 170
 

THE INFINITE DIVISIBILITY AND ORTHOGONAL POLYNOMIALS WITH A CONSTANT RECURSION FORMULA IN FREE PROBABILITY THEORY

Naoko Saitoh
Hiroaki Yoshida

Abstract: We calculate Voiculescu’s R -transform of the compactly supported probability measure on R induced from the orthogonal polynomials with a constant recursion formula, and investigate its infinite divisibility with respect to the additive free convolution. In the case of infinite divisibility, we give the Lévy-Hinčin measure explicitly for the integral representation of the R -transform of the free analogue of the Lévy-Hinčin formula.

1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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