Functions Inverse to Weakly Hyperbolic and Hyperbolic Pencils

A. I. Barsukov^a, O. G. Konyukhva<sup>b

a</sup> 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.

UDC: 512.643.8

Received: 08.04.2016
Revised: 25.05.2016

DOI: 10.4213/mzm11433

 English version: Mathematical Notes, 2017, 101:1, 48–57

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