Journal of Fourier Analysis and Applications

, Volume 3, Issue 3, pp 207–238

The uncertainty principle: A mathematical survey


  • Gerald B. Folland
    • Department of MathematicsUniversity of Washington
  • Alladi Sitaram
    • Statistics and Mathematics DivisionIndian Statistical Institute, R. V. College Post Office
Research Tutorial

DOI: 10.1007/BF02649110

Cite this article as:
Folland, G.B. & Sitaram, A. The Journal of Fourier Analysis and Applications (1997) 3: 207. doi:10.1007/BF02649110


We survey various mathematical aspects of the uncertainty principle, including Heisenberg’s inequality and its variants, local uncertainty inequalities, logarithmic uncertainty inequalities, results relating to Wigner distributions, qualitative uncertainty principles, theorems on approximate concentration, and decompositions of phase space.

Math Subject Classifications

Primary 42-02, 42B10, 26D15Secondary 43A25, 43A30, 81Q10, 81S30, 94A12, 94A17

Keywords and Phrases

uncertainty principleFourier transformHeisenberg’s inequalitylogarithmic inequalitiesWigner distributionLandau-Pollak-Slepian theoryphase space

Copyright information

© CRC Press, Inc 1997