THE INFINITE DIVISIBILITY AND ORTHOGONAL POLYNOMIALS
WITH A CONSTANT RECURSION FORMULA IN FREE PROBABILITY
THEORY
Naoko Saitoh
Hiroaki Yoshida
Abstract: We calculate Voiculescu’s -transform of the compactly supported probability
measure on 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 -transform of the free analogue of the Lévy-Hinčin formula.
1991 AMS Mathematics Subject Classification: Primary: -; Secondary: -;
Key words and phrases: -