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Sibirsk. Mat. Zh., 2004, Volume 45, Number 2, Pages 387–393 (Mi smj1076)  

This article is cited in 9 scientific papers (total in 9 papers)

Multiple Laurent series and difference equations

E. K. Leinartas

Krasnoyarsk State University

Abstract: Using the notion of amoeba of the characteristic polynomial of a difference equation, we obtain a description for the solution space of a multidimensional difference equation with constant coefficients.

Keywords: Laurent series, difference equation, Newton polyhedron, amoeba of a polynomial

Full text: PDF file (193 kB)
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English version:
Siberian Mathematical Journal, 2004, 45:2, 321–326

Bibliographic databases:

UDC: 517.55
Received: 19.05.2003

Citation: E. K. Leinartas, “Multiple Laurent series and difference equations”, Sibirsk. Mat. Zh., 45:2 (2004), 387–393; Siberian Math. J., 45:2 (2004), 321–326

Citation in format AMSBIB
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\by E.~K.~Leinartas
\paper Multiple Laurent series and difference equations
\jour Sibirsk. Mat. Zh.
\yr 2004
\vol 45
\issue 2
\pages 387--393
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2061418}
\zmath{https://zbmath.org/?q=an:1052.39002}
\transl
\jour Siberian Math. J.
\yr 2004
\vol 45
\issue 2
\pages 321--326
\crossref{https://doi.org/10.1023/B:SIMJ.0000021287.35640.87}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000220959600011}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. K. Leinartas, “Multiple Laurent series and fundamental solutions of linear difference equations”, Siberian Math. J., 48:2 (2007), 268–272  mathnet  crossref  mathscinet  zmath  isi
    2. E. K. Leinartas, M. Passare, A. K. Tsikh, “Multidimensional versions of Poincaré's theorem for difference equations”, Sb. Math., 199:10 (2008), 1505–1521  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. Pavel V. Trishin, “O meromorfnykh resheniyakh dvumernykh raznostnykh uravnenii”, Zhurn. SFU. Ser. Matem. i fiz., 2:3 (2009), 360–369  mathnet  elib
    4. Evgenii K. Leinartas, Aleksandr P. Lyapin, “O ratsionalnosti mnogomernykh vozvratnykh stepennykh ryadov”, Zhurn. SFU. Ser. Matem. i fiz., 2:4 (2009), 449–455  mathnet  elib
    5. Evgenii K. Leinartas, “Kriterii asimptoticheskoi ustoichivosti mnogomernogo raznostnogo uravneniya s postoyannymi koeffitsientami”, Zhurn. SFU. Ser. Matem. i fiz., 4:1 (2011), 112–117  mathnet  elib
    6. E. K. Leǐnartas, “Stability of the Cauchy problem for a multidimensional difference operator and the amoeba of the characteristic set”, Siberian Math. J., 52:5 (2011), 864–870  mathnet  crossref  mathscinet  isi
    7. Marina S. Rogozina, “Ustoichivost mnogosloinykh raznostnykh skhem i ameby algebraicheskikh giperpoverkhnostei”, Zhurn. SFU. Ser. Matem. i fiz., 5:2 (2012), 256–263  mathnet
    8. Marina S. Rogozina, “On the correctness of polynomial difference operators”, Zhurn. SFU. Ser. Matem. i fiz., 8:4 (2015), 437–441  mathnet  crossref
    9. Kytmanov A.A. Lyapin A.P. Sadykov T.M., “Evaluating the Rational Generating Function For the Solution of the Cauchy Problem For a Two-Dimensional Difference Equation With Constant Coefficients”, Program. Comput. Softw., 43:2 (2017), 105–111  crossref  mathscinet  isi  scopus
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