On the stability of the first-order linear recurrence in topological vector spaces

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• 作者：Mohammad Sal Moslehian ; Dorian Popa
• 关键词：Stability ; First-order linear recurrence ; Topological vector spaces ; Convex hull ; Balanced hull
• 刊名：Nonlinear Analysis
• 出版年：2010
• 出版时间：1 November 2010
• 年：2010
• 卷：73
• 期：9
• 页码：2792-2799
• 全文大小：266 K

文摘

Suppose that is a sequentially complete Hausdorff locally convex space over a scalar field , V is a bounded subset of , (a_n)_n≥0 is a sequence in with the property lim inf_n→∞a_n>1, and (b_n)_n≥0 is a sequence in . We show that for every sequence (x_n)_n≥0 in satisfying there exists a unique sequence (y_n)_n≥0 satisfying the recurrence , and for every q with 1<q<lim inf_n→∞a_n there exists such that