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

This article is cited in 2 scientific papers (total in 2 papers)

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  mathnet  crossref  crossref  mathscinet  isi  elib
    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  mathnet  crossref
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