| Journal of Siberian Federal University. Mathematics & Physics |
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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.
DOI: https://doi.org/10.17516/1997-1397-2018-11-6-712-722   Full text:
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UDC: 517.55+517.96 Received: 15.06.2018 Received in revised form: 20.08.2018 Accepted: 20.09.2018 Language: 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), 
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