Abstract:
Employing the notion of the amoeba of an algebraic set we state a multidimensional analog of the following condition: The moduli of roots of a polynomial are less than one. This analog is proved to be a necessary and sufficient condition for stability of the Cauchy problem for a polynomial difference operator with constant coefficients.
Keywords:multidimensional difference equation, amoeba of an algebraic surface, stability of the Cauchy problem.