Title

Balian-Low Phenomenon For Subspace Gabor Frames

Abstract

In this work, the Balian-Low theorem is extended to Gabor (also called Weyl-Heisenberg) frames for subspaces and, more particularly, its relationship with the unique Gabor dual property for subspace Gabor frames is pointed out. To achieve this goal, the subspace Gabor frames which have a unique Gabor dual of type I (resp. type II) are defined and characterized in terms of the Zak transform for the rational parameter case. This characterization is then used to prove the Balian-Low theorem for subspace Gabor frames. Along the same line, the same characterization is used to prove a duality theorem for the unique Gabor dual property which is an analogue of the Ron and Shen duality theorem. © 2004 American Institute of Physics.

Publication Date

8-1-2004

Publication Title

Journal of Mathematical Physics

Volume

45

Issue

8

Number of Pages

3362-3378

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1063/1.1768621

Socpus ID

4544320485 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/4544320485

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