Gabor Schauder bases and the Balian-Low Theorem

Series: 
Analysis Seminar
Monday, February 2, 2009 - 14:00
1 hour (actually 50 minutes)
Location: 
Skiles 255
,  
School of Mathematics, Georgia Tech
Organizer: 
The Balian-Low Theorem is a strong form of the uncertainty principle for Gabor systems that form orthonormal or Riesz bases for L^2(R). In this talk we will discuss the Balian-Low Theorem in the setting of Schauder bases. We prove that new weak versions of the Balian-Low Theorem hold for Gabor Schauder bases, but we constructively demonstrate that several variants of the BLT can fail for Gabor Schauder bases that are not Riesz bases. We characterize a class of Gabor Schauder bases in terms of the Zak transform and product A_2 weights; the Riesz bases correspond to the special case of weights that are bounded away from zero and infinity. This is joint work with Alex Powell (Vanderbilt University).