巴拿赫空间中线性离散时间系统的多项式二分性

On Polynomial Dichotomy of Linear Discrete-Time Systems in Banach Spaces

中文关键词:  线性离散时间系统  一致多项式二分性  多项式二分性

英文关键词:linear discrete-time systems  uniform polynomial dichotomy  polynomial dichotomy

中文摘要:

      本文给出了巴拿赫空间中线性差分方程的两个多项式二分性概念, 使其在相应空间中的范数的增长速度不快于指数型增长. 并用实例阐释了相关概念之间的关系. 借助于指数二分性的研究方法讨论了多项式二分性的特征, 所得结论推广了指数稳定性及指数二分性中的一些已有结果.

英文摘要:

      This paper deals with two concepts of polynomial dichotomy for linear difference equations which are defined in a Banach space and whose norms can increase not faster than exponentially. Some illustrating examples clarify the relations between these concepts. Our approach is based on the extension of techniques for exponential dichotomy to the case of polynomial dichotomy. The obtained results are generalizations of well-known theorems about the exponential stability and exponential dichotomy.