Gabor Schauder bases and the Balian-Low theorem
Gabor Schauder bases and the Balian-Low theorem
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Gabor Schauder 基底和 Balian-Low 定理
DOI：
10.1063/1.2360041
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发表时间：
2006
影响因子：
1.3
通讯作者：
A. Powell
中科院分区：
文献类型：
--
作者：
C. Heil;A. Powell
Balian-Low定理是Gabor系统的不确定性原理的一种强形式，它形成L2（R）的标准正交基或Riesz基。本文研究了Schauder基下的Balian-Low定理。我们证明，新的弱版本的巴利安低定理持有的Gabor Schauder基地，但我们建设性地证明，几个变种的BLT可以失败的Gabor Schauder基地，不是Riesz基地。利用Zak变换和乘积A2权刻画了一类Gabor Schauder基，Riesz基对应于权有界远离零和无穷大的特殊情况，Balian-Low定理是Gabor系统不确定性原理的一个强形式，它构成L2（R）的标准正交基或Riesz基.本文研究了Schauder基下的Balian-Low定理。我们证明，新的弱版本的巴利安低定理持有的Gabor Schauder基地，但我们建设性地证明，几个变种的BLT可以失败的Gabor Schauder基地，不是Riesz基地。我们刻画了一类Gabor Schauder基地的Zak变换和产品A2重量的Riesz基地对应的特殊情况下，有界远离零和无穷大的重量。
The Balian-Low Theorem is a strong form of the uncertainty principle for Gabor systems that form orthonormal or Riesz bases for L2(R). In this paper we investigate the Balian-Low Theorem in the setting of Schauder bases. We prove that new weak versions of the Balian-Low Theorem hold for Gabor Schauder bases, but we constructively demonstrate that several variants of the BLT can fail for Gabor Schauder bases that are not Riesz bases. We characterize a class of Gabor Schauder bases in terms of the Zak transform and product A2 weights; the Riesz bases correspond to the special case of weights that are bounded away from zero and infinity.The Balian-Low Theorem is a strong form of the uncertainty principle for Gabor systems that form orthonormal or Riesz bases for L2(R). In this paper we investigate the Balian-Low Theorem in the setting of Schauder bases. We prove that new weak versions of the Balian-Low Theorem hold for Gabor Schauder bases, but we constructively demonstrate that several variants of the BLT can fail for Gabor Schauder bases that are not Riesz bases. We characterize a class of Gabor Schauder bases in terms of the Zak transform and product A2 weights; the Riesz bases correspond to the special case of weights that are bounded away from zero and infinity.