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 Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 2014, Volume 14, Issue 3, Pages 83–94 (Mi vngu347)

On the Solvability of the Cauchy Problem for a Polynomial Difference Operator

M. S. Rogozina

Siberian Federal University, Krasnoyarsk

Abstract: In this paper we consider a variant of the Cauchy problem for a polynomial difference operator. A formula representing the solution to the problem via its fundamental solution is obtained, the conditions for its solvability are given. In particular, in two-dimensional case a rather simple condition in terms of coefficients of the operator symbol is proved. Besides that, a recurrence relation for principal minors of the matrix corresponding to the difference operator is obtained.

Keywords: difference operator, fundamental solution.

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English version:
Journal of Mathematical Sciences, 2016, 213:6, 887–896

UDC: 517.55, 519.111.1

Citation: M. S. Rogozina, “On the Solvability of the Cauchy Problem for a Polynomial Difference Operator”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 14:3 (2014), 83–94; J. Math. Sci., 213:6 (2016), 887–896

Citation in format AMSBIB
\Bibitem{Rog14} \by M.~S.~Rogozina \paper On the Solvability of the Cauchy Problem for a Polynomial Difference Operator \jour Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform. \yr 2014 \vol 14 \issue 3 \pages 83--94 \mathnet{http://mi.mathnet.ru/vngu347} \transl \jour J. Math. Sci. \yr 2016 \vol 213 \issue 6 \pages 887--896 \crossref{https://doi.org/10.1007/s10958-016-2749-6} 

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This publication is cited in the following articles:
1. Marina S. Rogozina, “On the correctness of polynomial difference operators”, Zhurn. SFU. Ser. Matem. i fiz., 8:4 (2015), 437–441
2. Marina S. Apanovich, Evgeny K. Leinartas, “Correctness of a two-dimensional Cauchy problem for a polynomial difference operator with constant coefficients”, Zhurn. SFU. Ser. Matem. i fiz., 10:2 (2017), 199–205
3. 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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