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Quaternion Fourier transform on quaternion fields and generalizations. (English) Zbl 1143.42006
Author’s abstract: We treat the quaternionic Fourier transform (QFT) applied to quaternion fields and investigate QFT properties useful for applications. Different forms of the QFT lead us to different Plancherel theorems. We relate the QFT computation for quaternion fields to the QFT of real signals. We research the general linear (GL) transformation behavior of the QFT with matrices, Clifford geometric algebra and with examples. We finally arrive at wide-ranging non-commutative multivector FT generalizations of the QFT. Examples given are new volume-time and spacetime algebra Fourier transformations.
MSC:
 42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 11R52 Quaternion and other division algebras: arithmetic, zeta functions