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The Balian-Low theorem for a new kind of Gabor system. (English) Zbl 1266.42075

The Balian-Low theorem is a very important result in time-frequency analysis. The authors establish the Balian-Low theorem for a new kind of Gabor systems. The proposed Gabor systems are a generalization of already existing cases. Moreover, the authors give some properties of the corresponding generalized Zak transform and provide some examples of the generalized Gabor systems. The topic of this paper is interesting and important to researchers working on both theoretical and practical aspects of time-frequency analysis, Fourier analysis and sampling theorems.

MSC:

42C15 General harmonic expansions, frames
33C90 Applications of hypergeometric functions
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
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