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Sibirsk. Mat. Zh., 2015, Volume 56, Number 1, Pages 111–121 (Mi smj2625)  

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

Solvability of the Cauchy problem for a polynomial difference operator and monomial bases for the quotients of a polynomial ring

E. K. Leĭnartas, M. S. Rogozina

Siberian Federal University, Krasnoyarsk, Russia

Abstract: We find solvability conditions for a Cauchy problem with a polynomial difference operator and, in particular, give an easy-to-check sufficient condition in terms of the coefficients of the principal symbol of the difference operator. The solvability of the Cauchy problem is shown to be equivalent to the existence of a monomial basis in the quotient ring of the polynomial ring by the ideal generated by the characteristic polynomial.

Keywords: polynomial difference operator, Cauchy problem, monomial basis for the quotient ring.

Full text: PDF file (320 kB)
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English version:
Siberian Mathematical Journal, 2015, 56:1, 92–100

Bibliographic databases:

UDC: 517.55+519.111.1
Received: 03.06.2014

Citation: E. K. Leǐnartas, M. S. Rogozina, “Solvability of the Cauchy problem for a polynomial difference operator and monomial bases for the quotients of a polynomial ring”, Sibirsk. Mat. Zh., 56:1 (2015), 111–121; Siberian Math. J., 56:1 (2015), 92–100

Citation in format AMSBIB
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\pages 111--121
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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. Marina S. Rogozina, “On the correctness of polynomial difference operators”, Zhurn. SFU. Ser. Matem. i fiz., 8:4 (2015), 437–441  mathnet  crossref
    2. 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
    3. Marina S. Apanovich, Evgeny K. Leinartas, “Correctness of a two-dimensional Cauchy problem for a polynomial difference operator with constant coefficients”, Zhurn. SFU. Ser. Matem. i fiz., 10:2 (2017), 199–205  mathnet  crossref
    4. T. I. Yakovleva, “Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones”, Siberian Math. J., 58:2 (2017), 363–372  mathnet  crossref  crossref  isi  elib  elib
    5. Evgeny K. Leinartas, Tatiana 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
    6. M. S. Apanovich, E. K. Leinartas, “On correctness of Cauchy problem for a polynomial difference operator with constant coefficients”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 26 (2018), 3–15  mathnet  crossref
    7. Evgeny K. Leinartas, Tatiana I. Yakovleva, “On formal solutions of the HörmanderТs initial-boundary value problem in the class of Laurent series”, Zhurn. SFU. Ser. Matem. i fiz., 11:3 (2018), 278–285  mathnet  crossref
    8. A. P. Lyapin, S. Chandragiri, “Generating functions for vector partition functions and a basic recurrence relation”, J. Differ. Equ. Appl., 25:7 (2019), 1052–1061  crossref  mathscinet  zmath  isi  scopus
    9. Alexander P. Lyapin, Sreelatha Chandragiri, “The Cauchy problem for multidimensional difference equations in lattice cones”, Zhurn. SFU. Ser. Matem. i fiz., 13:2 (2020), 187–196  mathnet  crossref
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