The Balian–Low Theorem for the Windowed Clifford–Fourier Transform

  • Yingxiong FuEmail author
  • Uwe Kähler
  • Paula Cerejeiras
Part of the Trends in Mathematics book series (TM)


In this chapter, we provide the definition of the Clifford–Zak transform associated with the discrete version of the kernel of a windowed Clifford– Fourier transform. We proceed with deriving several important properties of such a transform. Finally, we establish the Balian–Low theorem for a Clifford frame under certain natural assumptions on the window function.


Clifford–Zak transform Clifford frame Balian–Low theorem Clifford–Fourier transform windowed Clifford–Fourier transform. 


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© Springer Basel 2013

Authors and Affiliations

  1. 1.Hubei Key Laboratory of Applied MathematicsHubei UniversityWuhanChina
  2. 2.Faculty of Mathematics and Computer ScienceHubei UniversityWuhanChina
  3. 3.Department of MathematicsUniversity of AveiroAveiroPortugal

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