New Proof for Balian-Low Theorem of Nonlinear Gabor System. (6th November 2013)

• Record Type: Journal Article
• Authors: Yuan, D. H.; Yang, S. Z.; Zheng, X. W.; Shen, Y. F.
• Other Names: Rao T. S. S. R. K. Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 2013(2013)
• Publication Date: 2013-11-06
• Subjects: Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2013/530172
• Languages: English
• ISSNs: 0972-6802

Abstract

Abstract : The main purpose of this paper is to give a new proof of the Balian-Low theorem for Gabor system { e i m θ ( 2 π t ) g ( t − n ), m, n ∈ ℤ }, which is proposed by Fu et al. and associated with nonlinear Fourier atoms. To this end, we establish the relationships between spaces L 2 ( ℝ, d θ ) and L 2 ( ℝ ) . We also introduce the concept of frame associated with nonlinear Fourier atoms for L 2 ( ℝ, d θ ) and obtain many subsidiary results for this kind of (Gabor) frames.