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Эта публикация цитируется в 6 научных статьях (всего в 6 статьях)
Implicit linear nonhomogeneous difference equation in Banach and locally convex spaces
S. L. Gefter, A. L. Piven School Mathematics and Computer Sciences, V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv, 61022, Ukraine
Аннотация:
The subjects of this work are the implicit linear difference equations $Ax_{n+1}+Bx_n=g_n$ and $Ax_{n+1}=x_n-f_n, n=0,1,2,\ldots$, where $A$ and $B$ are continuous operators acting in certain locally convex spaces. The existence and uniqueness conditions, along with explicit formulas, are obtained for solutions of these equations. As an application of the general theory produced this way, the equation $Ax_{n+1}=x_n-f_n$ in the space $\mathbb{R}^{\infty}$ of finite sequences and in the space $\mathbb{R}^M$, where $M$ is an arbitrary set, has been studied.
Ключевые слова и фразы:
difference equation, locally convex space, Banach space, locally nilpotent operator.
Поступила в редакцию: 16.04.2018 Исправленный вариант: 15.11.2018
Образец цитирования:
S. L. Gefter, A. L. Piven, “Implicit linear nonhomogeneous difference equation in Banach and locally convex spaces”, Журн. матем. физ., анал., геом., 15:3 (2019), 336–353
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag731 https://www.mathnet.ru/rus/jmag/v15/i3/p336
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