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Gabor Schauder Bases and the Balian-Low Theorem
by
Christopher Heil
Georgia Institute of Technology
Coauthors: Alexander M. Powell (Vanderbilt University)
The Balian-Low Theorem is a strong form of the uncertainty principle for Gabor systems that form orthonormal or Riesz bases for L2(R). In this talk we consider the Balian-Low Theorem in the setting of Schauder bases. We prove that 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 A2 weights.
Date received: February 18, 2008
Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavq-56.