The Balian-Low theorem and regularity of Gabor systems

  • John J. Benedetto
  • Wojciech Czaja
  • Przemystaw Gadziński
  • Alexander M. Powell
Article

Abstract

For any positive real numbers A, B, and d satisfying the conditions\(\frac{1}{A} + \frac{1}{B} = 1\), d>2, we construct a Gabor orthonormal basis for L2(ℝ), such that the generating function g∈L2(ℝ) satisfies the condition:∫|g(x)|2(1+|x|A)/logd(2+|x|)dx < ∞ and\(\int_{\hat {\mathbb{R}}} {\left| {\hat g(\xi )} \right|^2 (1 + \left| \xi \right|^B )/\log ^d (2 + \left| \xi \right|)d\xi< \infty } \).

Math Subject Classifications

42C40 

Key Words and Phrases

Gabor orthonormal bases Balian-Low theorem Zak transform regularity of functions 

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Copyright information

© Mathematica Josephina, Inc. 2003

Authors and Affiliations

  • John J. Benedetto
    • 1
  • Wojciech Czaja
    • 1
    • 2
  • Przemystaw Gadziński
    • 2
  • Alexander M. Powell
    • 1
  1. 1.Department of MathematicsUniversity of MarylandCollege Park
  2. 2.Mathematical InstituteUniversity of WrocławWrocławPoland

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