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Spectral analysis of operator polynomials and higher-order difference operators

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Abstract

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.

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Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    A. G. Baskakov

  2. National Research University Higher School of Economics, Moscow, Russia

    V. D. Kharitonov

Authors
  1. A. G. Baskakov
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  2. V. D. Kharitonov
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Correspondence to A. G. Baskakov.

Additional information

Original Russian Text © A. G. Baskakov, V. D. Kharitonov, 2017, published in Matematicheskie Zametki, 2017, Vol. 101, No. 3, pp. 330–345.

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Baskakov, A.G., Kharitonov, V.D. Spectral analysis of operator polynomials and higher-order difference operators. Math Notes 101, 391–405 (2017). https://doi.org/10.1134/S0001434617030026

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  • DOI: https://doi.org/10.1134/S0001434617030026

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