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The Cauchy problem for multidimensional difference equations and the preservation of the hierarchy of generating functions of its solutions
Evgeny K. Leinartas, Tatiana I. Yakovleva Institute of Mathematics and Computer Science, Siberian Federal University, Svobodny, 79, Krasnoyarsk, 660041, Russia
Abstract:
We study the dependence of the properties of the generating function of the solution of the Cauchy problem on the properties of the generating function of the initial data for a difference equation with constant coefficients in a rational point cone. Conditions are found under which the generating functions of the solution remain in the same classes as the generating functions of the initial data.
Keywords:
multidimensional difference equations, Cauchy problem, hierarchy of generating function, Hadamard composition.
Funding Agency |
Grant Number |
Russian Foundation for Basic Research  |
18-31-00232 18-51-41011_Uzb_t |
The first author was supported by RFFI no. 18-51-41011 Uzb_t, and the second by RFBR
according to the research project no. 18-31-00232. |
DOI:
https://doi.org/10.17516/1997-1397-2018-11-6-712-722
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Bibliographic databases:
UDC:
517.55+517.96 Received: 15.06.2018 Received in revised form: 20.08.2018 Accepted: 20.09.2018
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Citation:
Evgeny K. Leinartas, Tatiana I. Yakovleva, “The Cauchy problem for multidimensional difference equations and the preservation of the hierarchy of generating functions of its solutions”, J. Sib. Fed. Univ. Math. Phys., 11:6 (2018), 712–722
Citation in format AMSBIB
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\paper The Cauchy problem for multidimensional difference equations and the preservation of the hierarchy of generating functions of its solutions
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2018
\vol 11
\issue 6
\pages 712--722
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\crossref{https://doi.org/10.17516/1997-1397-2018-11-6-712-722}
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http://mi.mathnet.ru/eng/jsfu719 http://mi.mathnet.ru/eng/jsfu/v11/i6/p712
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