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Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2021, Volume 61, Number 10, Pages 1610–1617
DOI: https://doi.org/10.31857/S0044466921100021 (Mi zvmmf11300) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Ordinary differential equations

Linear difference operators with coefficients in the form of infinite sequences

S. A. Abramova, M. A. Barkatoub, M. Petkovšekc

a Dorodnicyn Computing Centre, Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 119333, Moscow, Russia
b University of Limoges, CNRS, XLIM UMR 7252, MATHIS 123, 87060, Limoges cedex, France
c University of Ljubljana, Faculty of Mathematics and Physics, SI-1000, Ljubljana, Slovenia
Citations (5)
DOI: https://doi.org/10.31857/S0044466921100021
Abstract: Some properties of linear difference operators whose coefficients have the form of infinite two-sided sequences over a field of characteristic zero are considered. In particular, it is found that such operators are deprived of some properties that are natural for differential operators over differential fields. In addition, we discuss questions of the decidability of certain problems arising in connection with the algorithmic representation of infinite sequences.
Key words: linear difference equations, infinite sequences in the role of coefficients, annihilating operators, solution spaces, divisibility, common multiples of operators, undecidable problems.
Funding agency Grant number
Russian Foundation for Basic Research 19-01-00032-а
Ministry of Education, Science and Sport of Slovenia research programme P1-02
Abramov’s work was supported in part by the Russian Foundation for Basic Research (project no. 19-01-00032-a) and Petkovšek’s work was supported in part by the Ministry of Education, Science, and Sport of Slovenia (research program P1-02).
Received: 03.02.2021
Revised: 19.05.2021
Accepted: 09.06.2021
English version:
Computational Mathematics and Mathematical Physics, 2021, Volume 61, Issue 10, Pages 1582–1589
DOI: https://doi.org/10.1134/S0965542521100018
Bibliographic databases:
Document Type: Article
UDC: 517.929
Language: Russian
Citation: S. A. Abramov, M. A. Barkatou, M. Petkovšek, “Linear difference operators with coefficients in the form of infinite sequences”, Zh. Vychisl. Mat. Mat. Fiz., 61:10 (2021), 1610–1617; Comput. Math. Math. Phys., 61:10 (2021), 1582–1589
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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