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Mat. Zametki, 2017, Volume 101, Issue 3, Pages 330–345 (Mi mz11170)  

This article is cited in 2 scientific papers (total in 2 papers)

Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators

A. G. Baskakova, V. D. Kharitonovb

a Voronezh State University
b National Research University "Higher School of Economics" (HSE), Moscow

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.

Keywords: operator polynomial, difference operator, spectrum of an operator, kernel of an operator, image of an operator.

Funding Agency Grant Number
Russian Science Foundation 14-21-00066


DOI: https://doi.org/10.4213/mzm11170

Full text: PDF file (555 kB)
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English version:
Mathematical Notes, 2017, 101:3, 391–405

Bibliographic databases:

UDC: 517.984
Received: 09.03.2016

Citation: A. G. Baskakov, V. D. Kharitonov, “Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators”, Mat. Zametki, 101:3 (2017), 330–345; Math. Notes, 101:3 (2017), 391–405

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/mz/v101/i3/p330

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. G. Baskakov, V. B. Didenko, “On invertibility states of differential and difference operators”, Izv. Math., 82:1 (2018), 1–13  mathnet  crossref  crossref  adsnasa  isi  elib
    2. D. A. Zakora, “Exponential Stability of a Certain Semigroup and Applications”, Math. Notes, 103:5 (2018), 745–760  mathnet  crossref  crossref  isi  elib
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