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We establish some Balian-Low type results for Gabor spaces, which concern with discontinuity in some periodization of Zφ, where Zφ is the Zak transform of the window function φ ∈ L2 (ℝd). The results are compared with the case for shift-invariant spaces where the Zak transform is replaced by Fourier transform.
A Gabor space is a space generated by a discrete set of time-frequency shifted copies of a single window function. Starting from the question of whether a Gabor space contains additional time-frequency shifts of the window function we establish a new Balian-Low type result. This result extends (for example) the well established Amalgam Balian-Low Theorem in the one dimensional case. The Gabor spaces...
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