Rational Time-frequency Vector-Valued Subspace Gabor Frames and Balian-Low Theorem
Rational Time-frequency Vector-Valued Subspace Gabor Frames and Balian-Low Theorem
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DOI：
10.1142/s0219691313500136
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发表时间：
2013-04
期刊：
影响因子：
--
通讯作者：
Yun‐Zhang Li;Yan Zhang
中科院分区：
文献类型：
--
作者：
Yun‐Zhang Li;Yan Zhang
本文研究了具有有理时频积的向量值子空间Gabor框架。通过引入合适的Zak变换矩阵，我们刻画了向量值子空间Gabor框架、Riesz基和标准正交基。我们刻画了I型和II型Gabor算子的唯一性。利用这个唯一性结果，我们将经典的Balian-Low定理推广到向量值子空间Gabor框架。同时指出了Ron-Shen对偶原理对一般的向量值子空间Gabor框架不成立。
This paper addresses vector-valued subspace Gabor frames with rational time-frequency product. By introduction of a suitable Zak transform matrix, we characterize vector-valued subspace Gabor frames, Riesz bases and orthonormal bases. We characterize the uniqueness of Gabor duals of type I and type II. Using the uniqueness results, we extend the classical Balian-Low theorem to vector-valued subspace Gabor frames. We also point out Ron-Shen duality principe does not hold for a general vector-valued subspace Gabor frame.