Mawardi, Bahri; Hitzer, Eckhard S. M. Clifford Fourier transformation and uncertainty principle for the Clifford geometric algebra \(\mathrm{Cl}_{3,0}\). (English) Zbl 1133.42305 Adv. Appl. Clifford Algebr. 16, No. 1, 41-61 (2006). Summary: First, the basic concept of the vector derivative in geometric algebra is introduced. Second, beginning with the Fourier transform on a scalar function we generalize to a real Fourier transform on Clifford multivector-valued functions \((f:\mathbb{R}^3 \to \mathrm{Cl}_{3,0})\). Third, we show a set of important properties of the Clifford Fourier transform on \(\mathrm{Cl}_{3,0}\) such as differentiation properties, and the Plancherel theorem. Finally, we apply the Clifford Fourier transform properties for proving an uncertainty principle for \(\mathrm{Cl}_{3,0}\) multivector functions. Cited in 35 Documents MSC: 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 15A66 Clifford algebras, spinors Keywords:vector derivative; multivector-valued function; Clifford (geometric) algebra; Clifford Fourier transform; uncertainty principle PDFBibTeX XMLCite \textit{B. Mawardi} and \textit{E. S. M. Hitzer}, Adv. Appl. Clifford Algebr. 16, No. 1, 41--61 (2006; Zbl 1133.42305) Full Text: DOI