Free Subordination and Belinschi-Nica Semigroup

Arizmendi, Octavio; Hasebe, Takahiro

Complex analysis and operator theory, 2016, 10(3), 581-603

Permalink : https://hdl.handle.net/2115/64617

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アクセス権	open access
URI	https://hdl.handle.net/2115/64617
タイトル	Free Subordination and Belinschi-Nica Semigroup
著者	著者名 Arizmendi, Octavio
著者	著者名 Hasebe, Takahiro
言語	英語
キーワード	Free subordination
	Boolean stable law
	Monotone stable law
	Markov-Krein transform
発行日	2016-03
出版者	Springer
収録物名	Complex analysis and operator theory
巻(号)	10(3)
ページ	581-603
抄録	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.
資源タイプ	学術雑誌論文
出版タイプ	Accepted Manuscript
権利情報	The final publication is available at link.springer.com
PISSN	1661-8254
関連情報 (isVersionOf)	出版社版DOI https://doi.org/10.1007/s11785-015-0500-9