The Balian–Low theorem for symplectic lattices in higher dimensions

Gröchenig, Karlheinz; Han, Deguang; Heil, Christopher und Kutyniok, Gitta (September 2002): The Balian–Low theorem for symplectic lattices in higher dimensions. In: Applied and Computational Harmonic Analysis, Vol. 13, No. 2: pp. 169-176

Abstract

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.

• Item Type: Journal article
• Keywords: Balian-Low theorem; frames; Gabor systems; modulation spaces; symplectic; matrices; uncertainty principles; GABOR FRAMES; Mathematics; Applied; Physics; Mathematical
• Faculties: Mathematics, Computer Science and Statistics > Mathematics > Bavarian Chair for Mathematical Foundations of Artificial Intelligence
• Subjects: 500 Science > 510 Mathematics
• ISSN: 10635203
• Language: English