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Sibirskii Matematicheskii Zhurnal, 2011, Volume 52, Number 5, Pages 1087–1095 (Mi smj2260)  
This article is cited in 5 scientific papers (total in 5 papers)

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

E. K. Leĭnartas

Institute of Mathematics of the Siberian Federal University, Krasnoyarsk, Russia
Full-text PDF (302 kB) Citations (5)
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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.
Keywords: multidimensional difference equation, amoeba of an algebraic surface, stability of the Cauchy problem.
Received: 15.06.2010
English version:
Siberian Mathematical Journal, 2011, Volume 52, Issue 5, Pages 864–870
DOI: https://doi.org/10.1134/S0037446611050119
Bibliographic databases:
Document Type: Article
UDC: 517.55+517.965
Language: Russian
Citation: E. K. Leǐnartas, “Stability of the Cauchy problem for a multidimensional difference operator and the amoeba of the characteristic set”, Sibirsk. Mat. Zh., 52:5 (2011), 1087–1095; Siberian Math. J., 52:5 (2011), 864–870
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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