This article is cited in 12 papers

Constant coefficient linear difference equations on the rational cones of the integer lattice

E. K. Leĭnartas^a, T. I. Nekrasova

^a Siberian Federal University, Krasnoyarsk, Russia

Abstract: We obtain a sufficient solvability condition for Cauchy problems for a polynomial difference operator with constant coefficients. We prove that if the generating function of the Cauchy data of a homogeneous Cauchy problem lies in one of the classes of Stanley's hierarchy then the generating function of the solution belongs to the same class.

Keywords: higher-dimensional difference equations, Cauchy problem, generating function, $D$-finite Laurent series.

UDC: 517.55+517.96

Received: 10.11.2014

DOI: 10.17377/smzh.2016.57.108

 English version: Siberian Mathematical Journal, 2016, 57:1, 74–85

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