A Quantitative Balian-Low Theorem

作者：Nitzan Shahaf; Olsen Jan Fredrik^*

来源：Journal of Fourier Analysis and Applications, 2013, 19(5): 1078-1092.

DOI：10.1007/s00041-013-9289-y

• Balian-Low theorem
• Riesz bases
• Frames
• Gabor systems
• Time-frequency analysis
• Uncertainty principles
• Zak transform

We study functions generating Gabor Riesz bases on the integer lattice. The classical Balian-Low theorem (BLT) restricts the simultaneous time and frequency localization of such functions. We obtain a quantitative estimate on their Zak transform that extends both this result and the more general (p,q) Balian-Low theorem. Moreover, we establish a family of quantitative amalgam-type Balian-Low theorems that contain both the amalgam BLT and the classical BLT as special cases.

• 出版日期2013-10