Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774586 | Journal of Mathematical Analysis and Applications | 2017 | 25 Pages |
Abstract
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 L2(R). This solves one of the last few open questions for this system.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
M. Speckbacher, P. Balazs,