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FIXED POINT THEOREM FOR AN INFINITE TOEPLITZ MATRIX
Bulletin of the Australian Mathematical Society ( IF 0.7 ) Pub Date : 2020-11-09 , DOI: 10.1017/s0004972720001215
VYACHESLAV M. ABRAMOV

For an infinite Toeplitz matrix T with nonnegative real entries we find the conditions under which the equation $\boldsymbol {x}=T\boldsymbol {x}$ , where $\boldsymbol {x}$ is an infinite vector column, has a nontrivial bounded positive solution. The problem studied in this paper is associated with the asymptotic behaviour of convolution-type recurrence relations and can be applied to problems arising in the theory of stochastic processes and other areas.

中文翻译:

无限托普利兹矩阵的不动点定理

对于无限 Toeplitz 矩阵用非负实数我们找到方程的条件 $\boldsymbol {x}=T\boldsymbol {x}$ , 在哪里 $\boldsymbol {x}$ 是一个无限向量列,有一个非平凡的有界正解。本文研究的问题与卷积型递推关系的渐近行为有关,可应用于随机过程理论等领域出现的问题。
更新日期:2020-11-09
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