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Directional uncertainty principle for quaternion Fourier transform. (English) Zbl 1198.42006
Summary: This paper derives a new directional uncertainty principle for quaternion valued functions subject to the quaternion Fourier transformation. This can be generalized to establish directional uncertainty principles in Clifford geometric algebras with quaternion subalgebras. We demonstrate this with the example of a directional spacetime algebra function uncertainty principle related to multivector wave packets.
MSC:
42A38Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
15A66Clifford algebras, spinors
11R52Quaternion and other division algebras: arithmetic, zeta functions