Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone
We consider a multidimensional difference equation in a simplicial lattice cone with coefficients from a field of characteristic zero and sections of a generating series of a solution to the Cauchy problem for such equations. We use properties of the shift and projection operators on the integer lat...
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| Format: | Article |
| Language: | English |
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Irkutsk State University
2022-12-01
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| Series: | Известия Иркутского государственного университета: Серия "Математика" |
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| Online Access: | https://mathizv.isu.ru/en/article/file?id=1432 |
| _version_ | 1811179266021261312 |
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| author | A.P. Lyapin T. Cuchta |
| author_facet | A.P. Lyapin T. Cuchta |
| author_sort | A.P. Lyapin |
| collection | DOAJ |
| description | We consider a multidimensional difference equation in a simplicial lattice cone with coefficients from a field of characteristic zero and sections of a generating series of a solution to the Cauchy problem for such equations. We use properties of the shift and projection operators on the integer lattice $Z^{n}$ to find a recurrence relation (difference equation with polynomial coefficients) for the section of the generating series. This formula allows us to find a generating series of a solution to the Cauchy problem in the lattice cone through a generating series of its initial data and a right-side function of the difference equation. We derived an integral representation for sections of the holomorphic function, whose coefficients satisfy the difference equation with complex coefficients. Finally, we propose a system of differential equations for sections that represent D-finite functions of two complex variables. |
| first_indexed | 2024-04-11T06:32:58Z |
| format | Article |
| id | doaj.art-b62b7504e3cf411caad55001a8f62c89 |
| institution | Directory Open Access Journal |
| issn | 1997-7670 2541-8785 |
| language | English |
| last_indexed | 2024-04-11T06:32:58Z |
| publishDate | 2022-12-01 |
| publisher | Irkutsk State University |
| record_format | Article |
| series | Известия Иркутского государственного университета: Серия "Математика" |
| spelling | doaj.art-b62b7504e3cf411caad55001a8f62c892022-12-22T04:39:58ZengIrkutsk State UniversityИзвестия Иркутского государственного университета: Серия "Математика"1997-76702541-87852022-12-014217589https://doi.org/10.26516/1997-7670.2022.42.75Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial ConeA.P. LyapinT. CuchtaWe consider a multidimensional difference equation in a simplicial lattice cone with coefficients from a field of characteristic zero and sections of a generating series of a solution to the Cauchy problem for such equations. We use properties of the shift and projection operators on the integer lattice $Z^{n}$ to find a recurrence relation (difference equation with polynomial coefficients) for the section of the generating series. This formula allows us to find a generating series of a solution to the Cauchy problem in the lattice cone through a generating series of its initial data and a right-side function of the difference equation. We derived an integral representation for sections of the holomorphic function, whose coefficients satisfy the difference equation with complex coefficients. Finally, we propose a system of differential equations for sections that represent D-finite functions of two complex variables.https://mathizv.isu.ru/en/article/file?id=1432generating seriesdifference equationlattice conestanley hierarchysection |
| spellingShingle | A.P. Lyapin T. Cuchta Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone Известия Иркутского государственного университета: Серия "Математика" generating series difference equation lattice cone stanley hierarchy section |
| title | Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone |
| title_full | Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone |
| title_fullStr | Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone |
| title_full_unstemmed | Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone |
| title_short | Sections of the Generating Series of a Solution to a Difference Equation in a Simplicial Cone |
| title_sort | sections of the generating series of a solution to a difference equation in a simplicial cone |
| topic | generating series difference equation lattice cone stanley hierarchy section |
| url | https://mathizv.isu.ru/en/article/file?id=1432 |
| work_keys_str_mv | AT aplyapin sectionsofthegeneratingseriesofasolutiontoadifferenceequationinasimplicialcone AT tcuchta sectionsofthegeneratingseriesofasolutiontoadifferenceequationinasimplicialcone |