论文标题
LCA组的矩阵值GABOR框架用于操作员
Matrix-Valued Gabor Frames over LCA Groups for Operators
论文作者
论文摘要
g \ v avruta研究了原子系统的框架（即子空间），即$ k $ frames，其中较低的帧条件由有限的线性运算符$ k $的Hilbert-Adxoint控制。对于局部紧凑的Abelian G组和一个积极的整数$ n $，我们在矩阵值lebesgue space $ l^2（g，\ mathbb {c}^{c}^{n \ times n}）$中研究矩阵值的gabor系统框架N}）$控制不仅较低，而且控制上限条件。我们称此类帧矩阵价态$（θ，θ^*）$ - gabor框架。首先，我们讨论从不正常运算符方面保存映射的框架。其次，我们为存在矩阵值$（θ，θ^*）$ - Gabor帧的存在提供了必要的条件。结果表明，如果$θ$是可相邻的不正常运算符，则$ l^2（g，\ mathbb {c}^{n \ times n}）$允许A $λ$ -Tight $（θ，θ^*）$ - GABOR $ - GABOR $ - GABOR的每个正数$λ$。给出了矩阵值$（θ，θ^*）$ - Gabor帧的表征。最后，我们表明矩阵值$（θ，θ^*）$ - Gabor帧在窗口函数的小扰动下是稳定的。给出了几个例子来支持我们的研究。
G\v avruta studied atomic systems in terms of frames for range of operators (that is, for subspaces), namely $K$-frames, where the lower frame condition is controlled by the Hilbert-adjoint of a bounded linear operator $K$. For a locally compact abelian group G and a positive integer $n$, we study frames of matrix-valued Gabor systems in the matrix-valued Lebesgue space $L^2(G, \mathbb{C}^{n\times n})$ , where a bounded linear operator $Θ$ on $L^2(G, \mathbb{C}^{n\times n})$ controls not only lower but also the upper frame condition. We term such frames matrix-valued $(Θ, Θ^*)$-Gabor frames. Firstly, we discuss frame preserving mapping in terms of hyponormal operators. Secondly, we give necessary and sufficient conditions for the existence of matrix-valued $(Θ, Θ^*)$- Gabor frames in terms of hyponormal operators. It is shown that if $Θ$ is adjointable hyponormal operator, then $L^2(G, \mathbb{C}^{n\times n})$ admits a $λ$-tight $(Θ, Θ^*)$-Gabor frame for every positive real number $λ$. A characterization of matrix-valued $(Θ, Θ^*)$-Gabor frames is given. Finally, we show that matrix-valued $(Θ, Θ^*)$-Gabor frames are stable under small perturbation of window functions. Several examples are given to support our study.
