Functions and Analysis

    

Clifford Fourier Transform on Multivector Fields and Uncertainty Principles for Dimensions N = 2 (Mod 4) and N = 3 (Mod 4)

Authors: Eckhard Hitzer, Bahri Mawardi

First, the basic concepts of the multivector functions, vector differential and vector derivative in geometric algebra are introduced. Second, we dene a generalized real Fourier transform on Clifford multivector-valued functions ( f : R^n -> Cl(n,0), n = 2,3 (mod 4) ). Third, we show a set of important properties of the Clifford Fourier transform on Cl(n,0), n = 2,3 (mod 4) such as dierentiation properties, and the Plancherel theorem, independent of special commutation properties. Fourth, we develop and utilize commutation properties for giving explicit formulas for f x^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 (mod 4) multivector functions. Keywords: Vector derivative, multivector-valued function, Clifford (geometric) algebra, Clifford Fourier transform, uncertainty principle.

Comments: 24 Pages. 2 tables. Adv. App. Cliff. Alg. Vol. 18, S3,4, pp. 715-736 (2008). DOI: 10.1007/s00006-008-0098-3.

Download: PDF

Submission history

[v1] 2013-06-17 01:59:58

Unique-IP document downloads: 492 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.

comments powered by Disqus