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Plurisubharmonic noncommutative rational functions
Journal article   Open access   Peer reviewed

Plurisubharmonic noncommutative rational functions

Harry Dym, J. William Helton, Igor Klep, Scott McCullough and Jurij Volčič
Journal of mathematical analysis and applications, v 492(1), 124421
01 Dec 2020
url
https://doi.org/10.1016/j.jmaa.2020.124421View
Published, Version of Record (VoR) Restricted

Abstract

Convex function Free analysis Noncommutative rational function Plurisubharmonic function Realization
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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Mathematics
Mathematics, Applied
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