Clifford Fourier transform on multivector fields and uncertainty principles for dimensions
. (English) Zbl 1177.15029
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 (, ). Third, we show a set of important properties of the Clifford Fourier transform on , 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 , and for the Clifford convolution. Finally, we apply Clifford Fourier transform properties for proving an uncertainty principle for , multivector functions.
|15A66||Clifford algebras, spinors|
|43A32||Other transforms and operators of Fourier type|