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Recent Developments in the Balian-Low Theorem

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Harmonic Analysis and Applications

Part of the book series: Applied and Numerical Harmonic Analysis ((ANHA))

Abstract

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.

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Author information

Authors and Affiliations

  1. Institute of Mathematics, University of Wrocław, pl. Grunwaldzki 2/4, 50-384, Wrocław, Poland

    Wojciech Czaja

  2. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA

    Alexander M. Powell

  3. Department of Mathematics, University of Maryland, College Park, MD, 20742, USA

    Wojciech Czaja

Authors
  1. Wojciech Czaja
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  2. Alexander M. Powell
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Editor information

Editors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332-0160, USA

    Christopher Heil

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Czaja, W., Powell, A.M. (2006). Recent Developments in the Balian-Low Theorem. In: Heil, C. (eds) Harmonic Analysis and Applications. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/0-8176-4504-7_5

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