Calculation of particular solutions of nonhomogeneous linear equations with two linear operators, of which at least one is almost algebraic, in the case of simple roots of the characteristic equation
The concept of an operator is an almost algebraic with respect to two-sided ideal of the algebra of linear operators in some finite-dimensional linear spaces, it extended to the case when the ideal is left. We prove a theorem on the following equation particular solution $\sum\limits^{n, m}_{i=0, j=...
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Institute of Computer Science
2016-02-01
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| Series: | Компьютерные исследования и моделирование |
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| Online Access: | http://crm.ics.org.ru/uploads/crmissues/crm_2016_1/16.08.02.pdf |
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doaj-65ba8240ffdd4033a8b3eeab1c6b27aa2020-11-24T21:55:31ZrusInstitute of Computer ScienceКомпьютерные исследования и моделирование2076-76332077-68532016-02-018191810.20537/2076-7633-2016-8-1-9-182408Calculation of particular solutions of nonhomogeneous linear equations with two linear operators, of which at least one is almost algebraic, in the case of simple roots of the characteristic equationVladimir G. TsirulikThe concept of an operator is an almost algebraic with respect to two-sided ideal of the algebra of linear operators in some finite-dimensional linear spaces, it extended to the case when the ideal is left. We prove a theorem on the following equation particular solution $\sum\limits^{n, m}_{i=0, j=0} a_{ij} A^i B^j u = f$, where $A$ and $B$ is a linear operator, $f$ is an element of a linear space. The result is applied to the differential-difference equations.http://crm.ics.org.ru/uploads/crmissues/crm_2016_1/16.08.02.pdfalmost algebraic differential operatorsalmost algebraic difference operatorsleft regularizers of linear operatorsdifferential-difference operatorspartial solutions of inhomogeneous linear difference-differential equations |
| collection |
DOAJ |
| language |
Russian |
| format |
Article |
| sources |
DOAJ |
| author |
Vladimir G. Tsirulik |
| spellingShingle |
Vladimir G. Tsirulik Calculation of particular solutions of nonhomogeneous linear equations with two linear operators, of which at least one is almost algebraic, in the case of simple roots of the characteristic equation Компьютерные исследования и моделирование almost algebraic differential operators almost algebraic difference operators left regularizers of linear operators differential-difference operators partial solutions of inhomogeneous linear difference-differential equations |
| author_facet |
Vladimir G. Tsirulik |
| author_sort |
Vladimir G. Tsirulik |
| title |
Calculation of particular solutions of nonhomogeneous linear equations with two linear operators, of which at least one is almost algebraic, in the case of simple roots of the characteristic equation |
| title_short |
Calculation of particular solutions of nonhomogeneous linear equations with two linear operators, of which at least one is almost algebraic, in the case of simple roots of the characteristic equation |
| title_full |
Calculation of particular solutions of nonhomogeneous linear equations with two linear operators, of which at least one is almost algebraic, in the case of simple roots of the characteristic equation |
| title_fullStr |
Calculation of particular solutions of nonhomogeneous linear equations with two linear operators, of which at least one is almost algebraic, in the case of simple roots of the characteristic equation |
| title_full_unstemmed |
Calculation of particular solutions of nonhomogeneous linear equations with two linear operators, of which at least one is almost algebraic, in the case of simple roots of the characteristic equation |
| title_sort |
calculation of particular solutions of nonhomogeneous linear equations with two linear operators, of which at least one is almost algebraic, in the case of simple roots of the characteristic equation |
| publisher |
Institute of Computer Science |
| series |
Компьютерные исследования и моделирование |
| issn |
2076-7633 2077-6853 |
| publishDate |
2016-02-01 |
| description |
The concept of an operator is an almost algebraic with respect to two-sided ideal of the algebra of linear operators in some finite-dimensional linear spaces, it extended to the case when the ideal is left. We prove a theorem on the following equation particular solution $\sum\limits^{n, m}_{i=0, j=0} a_{ij} A^i B^j u = f$, where $A$ and $B$ is a linear operator, $f$ is an element of a linear space. The result is applied to the differential-difference equations. |
| topic |
almost algebraic differential operators almost algebraic difference operators left regularizers of linear operators differential-difference operators partial solutions of inhomogeneous linear difference-differential equations |
| url |
http://crm.ics.org.ru/uploads/crmissues/crm_2016_1/16.08.02.pdf |
| work_keys_str_mv |
AT vladimirgtsirulik calculationofparticularsolutionsofnonhomogeneouslinearequationswithtwolinearoperatorsofwhichatleastoneisalmostalgebraicinthecaseofsimplerootsofthecharacteristicequation |
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1725862156450136064 |