Geodesic
Functions Inverse to Weakly Hyperbolic and Hyperbolic Pencils
Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 31-42.

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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. 
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A. I. Barsukov; O. G. Konyukhva. Functions Inverse to Weakly Hyperbolic and Hyperbolic Pencils. Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 31-42. http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a2/

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