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Matematicheskie Zametki, 2017, Volume 101, Issue 1, Pages 31–42
DOI: https://doi.org/10.4213/mzm11433 (Mi mzm11433) 		 
Functions Inverse to Weakly Hyperbolic and Hyperbolic Pencils

A. I. Barsukova, O. G. Konyukhvab

a Voronezh State Academy of Building and Architecture
b Voronezh
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DOI: https://doi.org/10.4213/mzm11433
Abstract: Necessary and sufficient conditions under which a matrix-valued function of a complex argument is inverse to a weakly hyperbolic or a hyperbolic pencil are established. For hyperbolic pencils, a constructive description of the inverse functions in terms of their partial fraction expansion with matrix coefficients is presented.
Keywords: rational matrix functions, weakly hyperbolic matrix pencils, hyperbolic matrix pencils, root zones of a pencil, Nevanlinna functions.
Funding agency Grant number
Russian Foundation for Basic Research 15-01-05315-a
Received: 08.04.2016
Revised: 25.05.2016
English version:
Mathematical Notes, 2017, Volume 101, Issue 1, Pages 48–57
DOI: https://doi.org/10.1134/S0001434617010059
Bibliographic databases:
Document Type: Article
UDC: 512.643.8
Language: Russian
Citation: A. I. Barsukov, O. G. Konyukhva, “Functions Inverse to Weakly Hyperbolic and Hyperbolic Pencils”, Mat. Zametki, 101:1 (2017), 31–42; Math. Notes, 101:1 (2017), 48–57
Citation in format AMSBIB
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