New Proof for Balian-Low Theorem of Nonlinear Gabor System

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.