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Sibirsk. Mat. Zh., 2016, Volume 57, Number 1, Pages 98–112 (Mi smj2731)  

This article is cited in 3 scientific papers (total in 3 papers)

Constant coefficient linear difference equations on the rational cones of the integer lattice

E. K. Leĭnartasa, T. I. Nekrasova

a Siberian Federal University, Krasnoyarsk, Russia

Abstract: 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.

Keywords: higher-dimensional difference equations, Cauchy problem, generating function, $D$-finite Laurent series.

Funding Agency Grant Number
Ministry of Education and Science of the Russian Federation 14.Y26.31.0006
Russian Foundation for Basic Research 14-01-00-544
This research was done at Siberian Federal University and supported by the Government of the Russian Federation (Grant 14.Y26.31.0006). The first author was also supported by the Russian Foundation for Basic Research (Grant 14-01-00-544).


DOI: https://doi.org/10.17377/smzh.2016.57.108

Full text: PDF file (518 kB)
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English version:
Siberian Mathematical Journal, 2016, 57:1, 74–85

Bibliographic databases:

UDC: 517.55+517.96
Received: 10.11.2014

Citation: E. K. Leǐnartas, T. I. Nekrasova, “Constant coefficient linear difference equations on the rational cones of the integer lattice”, Sibirsk. Mat. Zh., 57:1 (2016), 98–112; Siberian Math. J., 57:1 (2016), 74–85

Citation in format AMSBIB
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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. O. A. Shishkina, “Mnogochleny Bernulli ot neskolkikh peremennykh i summirovanie monomov po tselym tochkam ratsionalnogo parallelotopa”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 16 (2016), 89–101  mathnet
    2. E. K. Leinartas, T. I. Yakovleva, “The Cauchy problem for multidimensional difference equations and the preservation of the hierarchy of generating functions of its solutions”, Zhurn. SFU. Ser. Matem. i fiz., 11:6 (2018), 712–722  mathnet  crossref  mathscinet  isi  scopus
    3. E. K. Leinartas, T. I. Yakovleva, “On formal solutions of hormander's initial-boundary value problem in the class of laurent series”, J. Sib. Fed. Univ.-Math. Phys., 11:3 (2018), 278–285  mathnet  crossref  mathscinet  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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