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Quaternion and Clifford Fourier Transforms and Wavelets pp 299–319Cite as

Birkhäuser

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

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Abstract

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.

Mathematics Subject Classification (2010). 15A66; 30G35.

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Author information

Authors and Affiliations

  1. Hubei Key Laboratory of Applied Mathematics, Hubei University, Wuhan, Hubei, China

    Yingxiong Fu

  2. Faculty of Mathematics and Computer Science, Hubei University, Wuhan, Hubei, China

    Yingxiong Fu

  3. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Yingxiong Fu, Uwe Kähler & Paula Cerejeiras

Authors
  1. Yingxiong Fu
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  2. Uwe Kähler
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  3. Paula Cerejeiras
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Corresponding author

Correspondence to Yingxiong Fu .

Editor information

Editors and Affiliations

  1. , Department of Material Science, International Christian University, Osawa 3-10-2Mitaka-shi, Tokyo, 181-8585, Japan

    Eckhard Hitzer

  2. School of Computer Science and, Electronic Engineering, University of Essex, Wivenhoe Park, Colchester, CO4 3SQ, United Kingdom

    Stephen J. Sangwine

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Fu, Y., Kähler, U., Cerejeiras, P. (2013). The Balian–Low Theorem for the Windowed Clifford–Fourier Transform. In: Hitzer, E., Sangwine, S. (eds) Quaternion and Clifford Fourier Transforms and Wavelets. Trends in Mathematics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0603-9_15

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