Uncertainty principle for the Clifford algebra \(Cl_{3, 0}\) based on Clifford Fourier transform. (English) Zbl 1087.15528
Simos, Theodore S. (ed.) et al., ICNAAM 2005. International conference on numerical analysis and applied mathematics 2005. Official conference of the European Society of Computational Methods in Sciences and Engineering (ESCMSE), Rhodes, Greek, September 16–20, 2005. Weinheim: Wiley-VCH (ISBN 3-527-40652-2/hbk). 922-925 (2005).
From the introduction: We adopt and expand the generalization of the Fourier transform in Clifford geometric algebra \({\mathcal G}_3\) recently suggested by J. Ebling and G. Scheuermann [Clifford Fourier transform on vector fields, IEEE Transactions on Visualization and Computer Graphics, 11 (4) (2005)]. We explicitly show detailed properties of the real Clifford geometric algebra Fourier transform, which we subsequently use to define and prove the uncertainty principle for \({\mathcal G}^3\) multivector functions.
For the entire collection see [Zbl 1074.65001].
For the entire collection see [Zbl 1074.65001].
MSC:
| 15A66 | Clifford algebras, spinors |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
