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Izvestiya: Mathematics, 2015, Volume 79, Issue 2, Pages 217–232
DOI: https://doi.org/10.1070/IM2015v079n02ABEH002740 (Mi im8248) 		 
This article is cited in 14 scientific papers (total in 14 papers)

Difference operators and operator-valued matrices of the second order

A. G. Baskakov, A. Yu. Duplishcheva

Voronezh State University
English version PDF (322 kB) Citations (14)
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DOI: https://doi.org/10.1070/IM2015v079n02ABEH002740
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 2014–2016 (project no. 1110).
Received: 29.04.2014
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2015, Volume 79, Issue 2, Pages 3–20
DOI: https://doi.org/10.4213/im8248
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 47B39, 46B45, 47A06, 47A53, 34D09
Language: English
Original paper language: Russian
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
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v79/i2/p3
    • This publication is cited in the following 14 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:1882
    Russian version PDF:496
    English version PDF:14
    References:122
    First page:106
     
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