Gabor Schauder Bases and the Balian–low Theorem

نویسندگان

  • CHRISTOPHER HEIL
  • ALEXANDER M. POWELL
چکیده

The Balian–Low Theorem is a strong form of the uncertainty principle for Gabor systems which form orthonormal or Riesz bases for L(R). In this paper we investigate 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 A2 weights; the Riesz bases correspond to the special case of weights that are bounded away from zero and infinity.

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تاریخ انتشار 2006