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Hokkaido University Collection of Scholarly and Academic Papers >
Graduate School of Science / Faculty of Science >
Peer-reviewed Journal Articles, etc >
Free Subordination and Belinschi-Nica Semigroup
| Title: | Free Subordination and Belinschi-Nica Semigroup |
| Authors: | Arizmendi, Octavio Browse this author | | Hasebe, Takahiro Browse this author |
| Keywords: | Free subordination | | Boolean stable law | | Monotone stable law | | Markov-Krein transform |
| Issue Date: | Mar-2016 |
| Publisher: | Springer |
| Journal Title: | Complex analysis and operator theory |
| Volume: | 10 |
| Issue: | 3 |
| Start Page: | 581 |
| End Page: | 603 |
| Publisher DOI: | 10.1007/s11785-015-0500-9 |
| 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. |
| Rights: | The final publication is available at link.springer.com |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/64617 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 長谷部 高広
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