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Journal of Function Spaces and Applications
Volume 2013, Article ID 530172, 7 pages
http://dx.doi.org/10.1155/2013/530172
Research Article

New Proof for Balian-Low Theorem of Nonlinear Gabor System

1Department of Mathematics, Hanshan Normal University, Chaozhou, Guangdong 521041, China
2Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China

Received 27 July 2013; Revised 24 September 2013; Accepted 25 September 2013

Academic Editor: T. S. S. R. K. Rao

Copyright © 2013 D. H. Yuan et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The main purpose of this paper is to give a new proof of the Balian-Low theorem for Gabor system , which is proposed by Fu et al. and associated with nonlinear Fourier atoms. To this end, we establish the relationships between spaces and . We also introduce the concept of frame associated with nonlinear Fourier atoms for and obtain many subsidiary results for this kind of (Gabor) frames.