Reproducing pairs and Gabor systems at critical density

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:455

Article

Speckbacher, M.¹  Balazs, P.¹ 

[1] Austrian Acad Sci, Acoust Res Inst, Wohllebengasse 12-14, A-1040 Vienna, Austria

关键词: Gabor systems;    Reproducing pairs;    Critical density;    Zak transform;    Balian-Low theorem;   

DOI  :  10.1016/j.jmaa.2017.05.079

来源: Elsevier

【 摘 要 】

We use the concept of reproducing pairs to study Gabor systems at critical density. First, we present a generalization of the Balian-Low theorem to the reproducing pairs setting. Then, we prove our main result that there exists a reproducing partner for the Gabor system of integer time-frequency shifts of the Gaussian. In other words, the coefficients for this Gabor expansion of a square integrable function can be calculated using inner products with an unstructured family of vectors in L-2(R). This solves one of the last few open questions for this system. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free