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