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Izv. RAN. Ser. Mat., 2015, Volume 79, Issue 2, Pages 3–20 (Mi izv8248)  

This article is cited in 10 scientific papers (total in 10 papers)

Difference operators and operator-valued matrices of the second order

A. G. Baskakov, A. Yu. Duplishcheva

Voronezh State University

Abstract: We study linear difference operators (equations) of the second order. We give conditions under which they are invertible or Fredholm and obtain asymptotic representations for solutions of homogeneous difference equations. Our main results are obtained by assigning an operator-valued matrix of the second order to the given operator and then using the theory of difference operators of the first order determined by these matrices.

Keywords: linear difference operator, invertible operator, spectrum of an operator, exponential dichotomy, invertibility state of a linear operator, asymptotic behaviour of solutions.

Funding Agency Grant Number
Russian Foundation for Basic Research 13-01-00378
14-01-31196
Russian Science Foundation 14-21-00066
Ministry of Education and Science of the Russian Federation 1110
This paper was written with the financial support of RFBR (grants nos. 13-01-00378, 14-01-31196), a grant of RSF (project no. 14-21-00066) and the Ministry of Science and Education of Russia within the framework of a government request in the sphere of scientific activity for 20142016 (project no. 1110).


DOI: https://doi.org/10.4213/im8248

Full text: PDF file (589 kB)
References: PDF file   HTML file

English version:
Izvestiya: Mathematics, 2015, 79:2, 217–232

Bibliographic databases:

UDC: 517.9
MSC: 47B39, 46B45, 47A06, 47A53, 34D09
Received: 29.04.2014

Citation: A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. RAN. Ser. Mat., 79:2 (2015), 3–20; Izv. Math., 79:2 (2015), 217–232

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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. Yu. Duplischeva, “O differentsialnykh operatorakh i matritsakh vtorogo poryadka”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 15:1 (2015), 31–37  mathnet  crossref  elib
    2. M. S. Bichegkuev, “Lyapunov Transformation of Differential Operators with Unbounded Operator Coefficients”, Math. Notes, 99:1 (2016), 24–36  mathnet  crossref  crossref  mathscinet  isi  elib
    3. A. G. Baskakov, V. D. Kharitonov, “Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators”, Math. Notes, 101:3 (2017), 391–405  mathnet  crossref  crossref  mathscinet  isi  elib
    4. A. G. Baskakov, L. Yu. Kabantsova, I. D. Kostrub, T. I. Smagina, “Linear differential operators and operator matrices of the second order”, Differ. Equ., 53:1 (2017), 8–17  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    5. L. Yu. Kabantsova, “Lineinye raznostnye uravneniya vtorogo poryadka v banakhovom prostranstve i rasscheplenie operatorov”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 17:3 (2017), 285–293  mathnet  crossref  elib
    6. 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
    7. D. B. Didenko, “Spectral Properties of the Operators $AB$ and $BA$”, Math. Notes, 103:2 (2018), 196–208  mathnet  crossref  crossref  isi  elib
    8. N. B. Uskova, G. V. Garkavenko, “Teorema o rasscheplenii lineinykh operatorov i asimptotika sobstvennykh znachenii raznostnykh operatorov s rastuschim potentsialom”, Sib. zhurn. chist. i prikl. matem., 18:1 (2018), 91–106  mathnet  crossref
    9. I. I. Strukova, “O nekotorykh svoistvakh pochti periodicheskikh na beskonechnosti funktsii iz odnorodnykh prostranstv”, Materialy Voronezhskoi zimneimatematicheskoi shkolySovremennye metody teorii funktsiii smezhnye problemy.28 yanvarya–2 fevralya 2019 g.Chast 2, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 171, VINITI RAN, M., 2019, 47–56  mathnet  crossref  elib
    10. L. Yu. Kabantsova, “Ob usloviyakh obratimosti raznostnykh operatorov”, Materialy Voronezhskoi zimneimatematicheskoi shkolySovremennye metody teorii funktsiii smezhnye problemy.28 yanvarya–2 fevralya 2019 g.Chast 2, Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 171, VINITI RAN, M., 2019, 94–101  mathnet  crossref  elib
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