Short NotesNo Access

A REMARK ON MONOTONIC CONVOLUTION

H. BERCOVICI

Mathematics Department, Indiana University, Bloomington, IN 47405, USA

https://doi.org/10.1142/S0219025705001871Cited by:4 (Source: Crossref)

Abstract

Muraki has shown that monotonic convolution of probability measures corresponds with composition of the reciprocal Cauchy transforms corresponding with these measures. We provide a new proof of this fact, not involving the combinatorics of moments.

Keywords:

AMSC: 46L53, 60B99, 60F99, 30E20, 60E10

References

U. Haagerup, Free Probability Theory, Waterloo, ON, 1995, Fields Inst. Commun. 12 (Amer. Math. Soc., 1997) pp. 127–148. Google Scholar
N. Muraki, Infin. Dim. Anal. Quantum Probab. Rel. Topics 4, 39 (2001). Link, Web of Science, Google Scholar
N. Muraki, Monotonic convolution and monotonic Lévy–Hinčin formula, preprint, 2000 . Google Scholar
D. Voiculescu, J. Funct. Anal. 66, 323 (1986). Crossref, Web of Science, Google Scholar