The Balian-Low Theorem For Symplectic Lattices In Higher Dimensions
Balian-Low theorem; Frames; Gabor systems; Modulation spaces; Symplectic matrices; Uncertainty principles
The Balian-Low theorem expresses the fact that time-frequency concentration is incompatible with non-redundancy for Gabor systems that form orthonormal or Riesz bases for L2(ℝ). We extend the Balian-Low theorem for Riesz bases to higher dimensions, obtaining a weak form valid for all sets of time-frequency shifts which form a lattice in ℝ2d, and a strong form valid for symplectic lattices in ℝ2d. For the orthonormal basis case, we obtain a strong form valid for general non-lattice sets which are symmetric with respect to the origin. © 2002 Elsevier Science (USA). All rights reserved.
Applied and Computational Harmonic Analysis
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Gröchenig, Karlheinz; Han, Deguang; and Heil, Christopher, "The Balian-Low Theorem For Symplectic Lattices In Higher Dimensions" (2002). Scopus Export 2000s. 2757.