Harmonic Analysis and Applications

Part of the series Applied and Numerical Harmonic Analysis pp 79-100

Recent Developments in the Balian-Low Theorem

  • Wojciech CzajaAffiliated withInstitute of Mathematics, University of WrocławDepartment of Mathematics, University of Maryland
  • , Alexander M. PowellAffiliated withDepartment of Mathematics, Vanderbilt University

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The Balian-Low Theorem is one of many manifestations of the uncertainty principle in harmonic analysis. Originally stated as a result on the poor time-frequency localization of generating functions of Gabor orthonormal bases, it has become a synonym for many general and abstract problems in time-frequency analysis. In this chapter we present some of the directions in which the Balian-Low Theorem has been extended in recent years.