Constant coefficient linear difference equations on the rational cones of the integer lattice
E. K. Leĭnartas, T. I. Nekrasova · Siberian Mathematical Journal · 2016
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.