| Some Properties of Causal Linear Time-Invariant (LTI) Operators on the Weighted $\ell_2$ Space |
| Received:September 19, 2014 Revised:March 04, 2015 |
| Key Words:
causal LTI operators weighted $\ell_2$ space two-operator approach
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11271059). |
| Author Name | Affiliation | | Naifeng GAN | School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China
School of Mathematics and Information Science, Anshan Normal University, Liaoning 114007, P. R. China | | Yufeng LU | School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China | | Liu LIU | School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China |
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| Abstract: |
| 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 $\mathbb{Z}$. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2015.06.009 |
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