The Balian-Low theorem for symplectic lattices in higher dimensions
Abbreviated Journal Title
Appl. Comput. Harmon. Anal.
Balian-Low theorem; frames; Gabor systems; modulation spaces; symplectic; matrices; uncertainty principles; GABOR FRAMES; Mathematics, Applied; Physics, Mathematical
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 L-2(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 R-2d, and a strong form valid for symplectic lattices in R-2d. For the orthonormal basis case, we obtain a strong form valid for general non-lattice sets which are symmetric with respect to the origin. (C) 2002 Elsevier Science (USA). All rights reserved.
Applied and Computational Harmonic Analysis
"The Balian-Low theorem for symplectic lattices in higher dimensions" (2002). Faculty Bibliography 2000s. 3235.