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Stability of the Cauchy problem for a multidimensional difference operator and the amoeba of the characteristic set

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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.

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Authors and Affiliations

  1. Institute of Mathematics of the Siberian Federal University, Krasnoyarsk, Russia

    E. K. Leĭnartas

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  1. E. K. Leĭnartas
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Correspondence to E. K. Leĭnartas.

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Original Russian Text Copyright © 2011 Leĭnartas E. K.

The author was supported by the Russian Foundation for Basic Research (Grant 11-01-00852) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grants NSh-7347.2010.1 and MO 2.1.1/4620).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 52, No. 5, pp. 1087–1095, September–October, 2011.

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Leĭnartas, E.K. Stability of the Cauchy problem for a multidimensional difference operator and the amoeba of the characteristic set. Sib Math J 52, 864–870 (2011). https://doi.org/10.1134/S0037446611050119

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  • DOI: https://doi.org/10.1134/S0037446611050119

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