$L^2(\mathbb{R})$上亚正规算子生成的波包帧
Wave packet frames generated by hyponormal operators on $L^2(\mathbb{R})$
摘要：
本文利用$L^2(\mathbb{R})$上的亚正规算子研究了波包系统的类框架性质。利用算子的相对亚正规性给出了系统成为$L^2(\mathbb{R})$中波包标架的充要条件。利用紧波包框架证明了亚正规算子的一个刻画。这与Djordjevi $\acute{c}$利用具有闭值域的有界线性算子的Moore-Penrose逆证明的方法不同。讨论了由亚正规算子生成的波包框架的线性组合。
英文摘要：
In this paper we study frame-like properties of a wave packet system by using hyponormal operators on $L^2(\mathbb{R})$. We present necessary and sufficient conditions in terms of relative hyponormality of operators for a system to be a wave packet frame in $L^2(\mathbb{R})$. A characterization of hyponormal operators by using tight wave packet frames is proved. This is different from a method proved by Djordjevi$\acute{c}$ by using the Moore-Penrose inverse of a bounded linear operator with a closed range. The linear combinations of wave packet frames generated by hyponormal operators are discussed.
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