Journal article
Plurisubharmonic noncommutative rational functions
Journal of mathematical analysis and applications, v 492(1), 124421
01 Dec 2020
Abstract
A noncommutative (nc) function in x1,…,xg,x1⁎,…,xg⁎ is called plurisubharmonic (plush) if its nc complex Hessian takes only positive semidefinite values on an nc neighborhood of 0. The main result of this paper shows that an nc rational function is plush if and only if it is a composite of a convex rational function with an analytic (no xj⁎) rational function. The proof is entirely constructive. Further, a simple computable necessary and sufficient condition for an nc rational function to be plush is given in terms of its minimal realization.
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Details
- Title
- Plurisubharmonic noncommutative rational functions
- Creators
- Harry Dym - Weizmann Institute of ScienceJ. William Helton - University of California San DiegoIgor Klep - University of LjubljanaScott McCullough - University of FloridaJurij Volčič - Texas A&M University
- Publication Details
- Journal of mathematical analysis and applications, v 492(1), 124421
- Publisher
- Elsevier
- Grant note
- DMS 1954709 / NSF (https://doi.org/10.13039/100000001) SCHW 1723/1-1 / Deutsche Forschungsgemeinschaft (https://doi.org/10.13039/501100001659) DMS 1500835 / NSF (https://doi.org/10.13039/100000001) J1-8132; N1-0057; P1-0222 / Slovenian Research Agency (https://doi.org/10.13039/501100004329) DMS-1764231 / NSF (https://doi.org/10.13039/100000001) Royal Society of New Zealand (https://doi.org/10.13039/501100001509)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000564539000032
- Scopus ID
- 2-s2.0-85088630936
- Other Identifier
- 991021861883204721
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- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Mathematics
- Mathematics, Applied