学術雑誌論文 Free Subordination and Belinschi-Nica Semigroup

Arizmendi, Octavio  ,  Hasebe, Takahiro

10 ( 3 )  , pp.581 - 603 , 2016-03 , Springer
ISSN:1661-8254
内容記述
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.
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http://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/64617/1/ArizmendiHasebe-CAOT-Springer.pdf

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