Uncertainty principle for clifford geometric algebras Cln,0, n = 3 (mod 4) based on clifford fourier transform

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 : ℝn → 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.

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