论文标题
无限toeplitz矩阵的固定点定理
Fixed point theorem for an infinite Toeplitz matrix
论文作者
论文摘要
对于无限toeplitz矩阵$ t $，我们找到了条件，在该条件下，方程$ \ boldsymbol {x} = t \ boldsymbol {x} $，其中$ \ boldsymbol {x} $是无限的矢量矢量颜色，具有无限制的阳性解决方案。本文研究的问题与卷积类型复发关系的渐近行为有关，并且可以应用于随机过程理论和其他领域的应用问题中产生的不同问题。
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 behavior of convolution type recurrence relations, and can be applied to different problems arising in the theory of stochastic processes and applied problems from other areas.
