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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.
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English version:
Siberian Mathematical Journal, 2015, 56:1, 92–100
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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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Marina S. Rogozina, “On the correctness of polynomial difference operators”, Zhurn. SFU. Ser. Matem. i fiz., 8:4 (2015), 437–441
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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
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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
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T. I. Yakovleva, “Well-posedness of the Cauchy problem for multidimensional difference equations in rational cones”, Siberian Math. J., 58:2 (2017), 363–372
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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
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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
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Evgeny K. Leinartas, Tatiana I. Yakovleva, “On formal solutions of the Hörmander’s initial-boundary value problem in the class of Laurent series”, Zhurn. SFU. Ser. Matem. i fiz., 11:3 (2018), 278–285
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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
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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
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