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This article is cited in 6 scientific papers (total in 6 papers)
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
Abstract:
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.
Key words and phrases:
difference equation, locally convex space, Banach space, locally nilpotent operator.
Received: 16.04.2018 Revised: 15.11.2018
Citation:
S. L. Gefter, A. L. Piven, “Implicit linear nonhomogeneous difference equation in Banach and locally convex spaces”, Zh. Mat. Fiz. Anal. Geom., 15:3 (2019), 336–353
Linking options:
https://www.mathnet.ru/eng/jmag731 https://www.mathnet.ru/eng/jmag/v15/i3/p336
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Abstract page: | 61 | Full-text PDF : | 58 | References: | 10 |
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