Geodesic
Implicit linear nonhomogeneous difference equation in Banach and locally convex spaces
Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 3, pp. 336-353 Cet article a éte moissonné depuis la source Math-Net.Ru

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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. 
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S. L. Gefter; A. L. Piven. Implicit linear nonhomogeneous difference equation in Banach and locally convex spaces. Žurnal matematičeskoj fiziki, analiza, geometrii, Tome 15 (2019) no. 3, pp. 336-353. http://geodesic.mathdoc.fr/item/JMAG_2019_15_3_a2/

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