Geodesic
Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators
Matematičeskie zametki, Tome 101 (2017) no. 3, pp. 330-345.

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The study of the spectral properties of operator polynomials is reduced to the study of the spectral properties of the operator specified by the operator matrix. The results obtained are applied to higher-order difference operators. Conditions for their invertibility and for them to be Fredholm, as well as the asymptotic representation for bounded solutions of homogeneous difference equations are obtained.
Keywords: operator polynomial, difference operator, spectrum of an operator, kernel of an operator, image of an operator. 
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A. G. Baskakov; V. D. Kharitonov. Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators. Matematičeskie zametki, Tome 101 (2017) no. 3, pp. 330-345. http://geodesic.mathdoc.fr/item/MZM_2017_101_3_a1/

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