The Balian–Low theorem for symplectic lattices in higher dimensions

✍ Scribed by Karlheinz Gröchenig; Deguang Han; Christopher Heil; Gitta Kutyniok

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 109 KB
• Volume: 13
• Category: Article
• ISSN: 1063-5203
• DOI: 10.1016/s1063-5203(02)00506-7

✦ Synopsis

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.