Free Subordination and Belinschi-Nica Semigroup
Abstract
We realize the Belinschi-Nica semigroup of homomorphisms as a free multiplicative subordination. This realization allows to define more general semigroups of homomorphisms with respect to free multiplicative convolution. For these semigroups we show that a differential equation holds, generalizing the complex Burgers equation. We give examples of free multiplicative subordination and find a relation to the Markov-Krein transform, Boolean stable laws and monotone stable laws. A similar idea works for additive subordination, and in particular we study the free additive subordination associated to the Cauchy distribution and show that it is a homomorphism with respect to monotone, Boolean and free additive convolutions.
Cite
@article{arxiv.1408.5983,
title = {Free Subordination and Belinschi-Nica Semigroup},
author = {Octavio Arizmendi and Takahiro Hasebe},
journal= {arXiv preprint arXiv:1408.5983},
year = {2016}
}
Comments
21 pages, minor corrections, Complex Analysis and Operator Theory, First online: 16 October 2015