Hitzer, Eckhard M. S.; Mawardi, Bahri Clifford Fourier transform on multivector fields and uncertainty principles for dimensions \(n=2\pmod 4\) and \(n=3\pmod 4\). (English) Zbl 1177.15029 Adv. Appl. Clifford Algebr. 18, No. 3-4, 715-736 (2008). Summary: 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 (\(f :\mathbb{R}^n\to Cl_{n,0}\), \(n=2, 3\pmod 4\)). Third, we show a set of important properties of the Clifford Fourier transform on \(Cl _{n,0}\), \(n=2, 3 \pmod 4\) such as differentiation properties, and the Plancherel theorem, independent of special commutation properties. Fourth, we develop and utilize commutation properties for giving explicit formulas for \(fx^m\), \(f\nabla^m\) and for the Clifford convolution. Finally, we apply Clifford Fourier transform properties for proving an uncertainty principle for \(Cl _{n,0}\), \(n = 2, 3\pmod 4\) multivector functions. Cited in 53 Documents MSC: 15A66 Clifford algebras, spinors 43A32 Other transforms and operators of Fourier type Keywords:vector derivative; multivector-valued function; Clifford (geometric) algebra; Clifford Fourier transform; uncertainty principle; Clifford convolution PDFBibTeX XMLCite \textit{E. M. S. Hitzer} and \textit{B. Mawardi}, Adv. Appl. Clifford Algebr. 18, No. 3--4, 715--736 (2008; Zbl 1177.15029) Full Text: DOI