Geodesic
The Cauchy problem for multidimensional difference equations and the preservation of the hierarchy of generating functions of its solutions
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 712-722

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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
Mots-clés : Hadamard composition. 
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     title = {The {Cauchy} problem for multidimensional difference equations and the preservation of the hierarchy of generating functions of its solutions},
     journal = {\v{Z}urnal Sibirskogo federalʹnogo universiteta. Matematika i fizika},
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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. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 6, pp. 712-722. http://geodesic.mathdoc.fr/item/JSFU_2018_11_6_a6/