E.M.S. Hitzer, B. Mawardi
Uncertainty Principle for Clifford Geometric Algebras Cl_{n,0} , n = 3 (mod 4) based on Clifford Fourier Transform
in T. Qian, M.I. Vai, X.Yusheng (eds.), Wavelet Analysis and Applications, Springer (SCI) Book Series Applied and Numerical Harmonic Analysis, Springer (2006), pp. 45-54.

Abstract: First, the basic concepts of the multivector functions, vector differential and vector derivative in geometric algebra are introduced. Second, we define a generalized real Fourier transform on Clifford multivector-valued functions (f: R^n --> Cl_{n,0} , n = 3 (mod 4)). Third, we introduce a set of important properties of the Clifford Fourier transform on Cl_{n,0} , n = 3 (mod 4) such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving a directional uncertainty principle for Cl_{n,0} , n = 3 (mod 4) multivector functions.

Mathematics Subject Classification (2000). Primary 15A66; Secondary 43A32.

Keywords. Vector derivative, multivector-valued function, Clifford (geometric) algebra, Clifford Fourier transform, uncertainty principle.

The original publication will be available at www.springerlink.com.

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[Geometric Calculus Japan index]