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ON THE MULTIPLICATIVE PROPERTY OF DEFINING POLYNOMIALS
- Authors: Abramov S.A1
-
Affiliations:
- Dorodnitsyn Computing Center, Federal Research Center Computer Science and Control, RAS
- Issue: Vol 64, No 9 (2024)
- Pages: 1661-1666
- Section: Ordinary differential equations
- URL: https://journal-vniispk.ru/0044-4669/article/view/277176
- DOI: https://doi.org/10.31857/S0044466924090067
- EDN: https://elibrary.ru/WKRNUK
- ID: 277176
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Abstract
The roots of the indicial polynomial constructed for a given linear ordinary differential operator provide information about the features of solutions of the corresponding homogeneous differential equation. Operators and equations whose coefficients are formal Laurent series are discussed. Solutions of the same kind are considered. These assumptions describe the structure of the indicial polynomial of the product of differential operators. This structural (multiplicative) property is preserved in the case of converging series.
About the authors
S. A Abramov
Dorodnitsyn Computing Center, Federal Research Center Computer Science and Control, RAS
Email: sergeyabramov@mail.ru
Moscow, Russia
References
- Коддингтон Э.А., Левинсон Н. Теория обыкновенных дифференциальных уравнений. М.: Изд-во иностр. лит., 1958.
- Туганбаев А.А. Теория колец. Арифметические модули и кольца. М.: МЦНМО, 2009.
- Картан А. Элементарная теория аналитических функций одного и нескольких комплексных переменных. М.: Изд-во иностр. лит., 1963.
- Henrici P. Applied and computational complex analysis. Vol. 1. John Willey & Sons, 1974.
- Abramov S. EG—eliminations // J. of Difference Equations and Applications. 1999. V 5. P. 393—433.
- Abramov S., Petkovsek M., Ryabenko A. Special formal series solutions of linear operator equations // Discrete Math. 2000. V 210. P 3-25.
- Maple online help: http://www.maplesoft.com/support/help/
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