权重$l_2$空间上关联线性时不变算子的性质

Some Properties of Causal Linear Time-Invariant (LTI) Operators on the Weighted $\ell_2$ Space

中文关键词:  关联线性时不变算子  权重$\ell_2$空间  两算子方法

英文关键词:causal LTI operators  weighted $\ell_2$ space  two-operator approach

中文摘要:

      本文讨论了选取不同类型权重序列$\{w(t)\}_{t\in \mathbb{Z}}$时,权重$l_2(\mathbb{Z},w)$空间上关联线性时不变算子的性质,同时还讨论了非稳定关联线性时不变卷积算子的可闭性的有关问题,提出了关于线性时不变算子一些新的问题,并指出可在一大类权重$l_2(\mathbb{Z},w)$空间上进行鲁棒设计.

英文摘要:

      We discuss the properties of causal LTI operators on weighted $\ell_2$ spaces for different choices of the weighting sequence $\{w(t)\}_{t\in \mathbb{Z}}$. Problems of closability of unstable causal LTI convolution operators are also discussed. We shall provide a new type of argument concerning causal LTI operators and robust design that can be applied to a large class of weighted $\ell_2$ spaces on $\mathbb{Z}$.