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 J. Sib. Fed. Univ. Math. Phys., 2018, Volume 11, Issue 6, Pages 712–722 (Mi jsfu719)

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 18-31-0023218-51-41011_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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UDC: 517.55+517.96
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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