Linear Independence of Finite Gabor Systems Determined by Behavior at Infinity

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• 作者：John J. Benedetto (1)
  Abdelkrim Bourouihiya (2)
  
  1. Norbert Wiener Center ; Department of Mathematics ; University of Maryland ; College Park ; MD ; 20742 ; USA
  2. Nova Southeastern University ; 3301 College Avenue ; Fort Lauderdale ; FL ; 33314 ; USA
  
• 关键词：Gabor systems ; HRT conjecture ; Hardy fields ; Kronecker鈥檚 theorem ; 42 ; 46
• 刊名：Journal of Geometric Analysis
• 出版年：2015
• 出版时间：January 2015
• 年：2015
• 卷：25
• 期：1
• 页码：226-254
• 全文大小：414 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Differential Geometry
  Convex and Discrete Geometry
  Fourier Analysis
  Abstract Harmonic Analysis
  Dynamical Systems and Ergodic Theory
  Global Analysis and Analysis on Manifolds
  
• 出版者：Springer New York
• ISSN：1559-002X

文摘

We prove that the HRT (Heil, Ramanathan, and Topiwala) conjecture holds for finite Gabor systems generated by square-integrable functions with certain behavior at infinity. These functions include functions ultimately decaying faster than any exponential function, as well as square-integrable functions ultimately analytic and whose germs are in a Hardy field that is closed under translations. Two classes of the latter type of functions are the set of square-integrable logarithmico-exponential functions and the set of square-integrable Pfaffian functions. We also prove the HRT conjecture for certain finite Gabor systems generated by positive functions.