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 The Bulletin of Irkutsk State University. Series Mathematics, 2014, Volume 9, Pages 91–102 (Mi iigum202)

On the Hierarchy of Generating Functions for Solutions of Multidimensional Difference Equations

T. I. Nekrasova

Siberian Federal University, 79, Svobodny Prospect, Krasnoyarsk, 660041

Abstract: In this paper we study generating functions of solutions for a difference equation with the support in a rational cone of the lattice. For Laurent series with the support in such cone we define the notion of D-finiteness and find the sufficient condition, when rationality (algebraicity, D-finiteness) of the generating function of the solution to the Cauchy problem follows from rationality (algebraicity, D-finiteness) of the generating function of its initial data.

Keywords: multidimensional difference equations, Cauchy problem, generating function, D-finite Laurent series.

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Citation: T. I. Nekrasova, “On the Hierarchy of Generating Functions for Solutions of Multidimensional Difference Equations”, The Bulletin of Irkutsk State University. Series Mathematics, 9 (2014), 91–102

Citation in format AMSBIB
\Bibitem{Nek14} \by T.~I.~Nekrasova \paper On the Hierarchy of Generating Functions for Solutions of Multidimensional Difference Equations \jour The Bulletin of Irkutsk State University. Series Mathematics \yr 2014 \vol 9 \pages 91--102 \mathnet{http://mi.mathnet.ru/iigum202} 

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This publication is cited in the following articles:
1. E. K. Leǐnartas, T. I. Nekrasova, “Constant coefficient linear difference equations on the rational cones of the integer lattice”, Siberian Math. J., 57:1 (2016), 74–85
2. M. S. Apanovich, E. K. Leinartas, “On correctness of Cauchy problem for a polynomial difference operator with constant coefficients”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 26 (2018), 3–15
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