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Mat. Zametki, 2017, Volume 101, Issue 1, Pages 31–42 (Mi mz11433)  

Functions Inverse to Weakly Hyperbolic and Hyperbolic Pencils

A. I. Barsukova, O. G. Konyukhvab

a Voronezh State Academy of Building and Architecture
b Voronezh

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


DOI: https://doi.org/10.4213/mzm11433

Full text: PDF file (457 kB)
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English version:
Mathematical Notes, 2017, 101:1, 48–57

Bibliographic databases:

UDC: 512.643.8
Received: 08.04.2016
Revised: 25.05.2016

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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