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.
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).
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
\Bibitem{LeiNek16}
\by E.~K.~Le{\v\i}nartas, T.~I.~Nekrasova
\paper Constant coefficient linear difference equations on the rational cones of the integer lattice
\jour Sibirsk. Mat. Zh.
\yr 2016
\vol 57
\issue 1
\pages 98--112
\mathnet{http://mi.mathnet.ru/smj2731}
\crossref{https://doi.org/10.17377/smzh.2016.57.108}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3499854}
\elib{https://elibrary.ru/item.asp?id=26236932}
\transl
\jour Siberian Math. J.
\yr 2016
\vol 57
\issue 1
\pages 74--85
\crossref{https://doi.org/10.1134/S0037446616010080}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000373234400008}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85008502163}
Linking options:
https://www.mathnet.ru/eng/smj2731
https://www.mathnet.ru/eng/smj/v57/i1/p98
This publication is cited in the following 10 articles:
S. Chandragiri, “Riordan Arrays and Difference Equations of Subdiagonal Lattice Paths”, Sib Math J, 65:2 (2024), 411
A. B. Leinartene, A. P. Lyapin, “Applying Computer Algebra Systems to Study Chaundy-Bullard Identities for the Vector Partition Function with Weight”, Program Comput Soft, 50:2 (2024), 176
A. B. Leinartene, A. P. Lyapin, “Applying computer algebra systems to study Chaundy-Bullard identities for the vector partition function with weight”, Programmirovanie, 2024, no. 2, 79
Luis M. Sánchez-Ruiz, Sanjib Kumar Datta, Nityagopal Biswas, Matilde Legua, “Picturing the Growth Order of Solutions in Complex Linear Differential–Difference Equations with Coefficients of φ-Order”, Axioms, 12:3 (2023), 239
E. K. Leinartas, T. I. Yakovleva, “Proizvodyaschaya funktsiya resheniya raznostnogo uravneniya i mnogogrannik Nyutona kharakteristicheskogo mnogochlena”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 40 (2022), 3–14
A. P. Lyapin, T. Cuchta, “Sections of the generating series of a solution to a difference equation in a simplicial cone”, Izvestiya Irkutskogo gosudarstvennogo universiteta. Seriya Matematika, 42 (2022), 75–89
A. P. Lyapin, Sreelatha Chandragiri, “the Cauchy Problem For Multidimensional Difference Equations in Lattice Cones”, J. Sib. Fed. Univ.-Math. Phys., 13:2 (2020), 187–196
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
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
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
Citation in format AMSBIB
Contact us: