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 J. Sib. Fed. Univ. Math. Phys., 2015, Volume 8, Issue 2, Pages 184–191 (Mi jsfu420)

On the Cauchy problem for multidimensional difference equations in rational cone

Tatiana I. Nekrasova

Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia

Abstract: The Cauchy problem for multidimensional difference equations in rational cone is formulated and sufficient condition for its solvability is given. The notion of multisection of multiple Laurent series with the support in a rational cone is defined. The formulae which express any multisection through original series are presented.

Keywords: Cauchy problem, rational cone, generating function, multisection.

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UDC: 517.55
Accepted: 28.04.2015
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Citation: Tatiana I. Nekrasova, “On the Cauchy problem for multidimensional difference equations in rational cone”, J. Sib. Fed. Univ. Math. Phys., 8:2 (2015), 184–191

Citation in format AMSBIB
\Bibitem{Nek15} \by Tatiana~I.~Nekrasova \paper On the Cauchy problem for multidimensional difference equations in~rational cone \jour J. Sib. Fed. Univ. Math. Phys. \yr 2015 \vol 8 \issue 2 \pages 184--191 \mathnet{http://mi.mathnet.ru/jsfu420} 

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This publication is cited in the following articles:
1. T. I. Yakovleva, “Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones”, Siberian Math. J., 58:2 (2017), 363–372
2. M. Scheicher, “Gröbner bases and their application to the Cauchy problem on finitely generated affine monoids”, J. Symb. Comput., 80:2 (2017), 416–450
3. E. K. Leinartas, T. I. Yakovleva, “On formal solutions of the Hörmander’s initial-boundary value problem in the class of Laurent series”, J. Sib. Fed. Univ.-Math. Phys., 11:3 (2018), 278–285
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