This article is cited in 6 papers

Ordinary differential equations

Linear difference operators with coefficients in the form of infinite sequences

S. A. Abramov^a, M. A. Barkatou^b, M. Petkovšek<sup>c

a</sup> 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

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.

UDC: 517.929

Received: 03.02.2021
Revised: 19.05.2021
Accepted: 09.06.2021

DOI: 10.31857/S0044466921100021

 English version: Computational Mathematics and Mathematical Physics, 2021, 61:10, 1582–1589

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