E.M.S. Hitzer

in S.L. Eriksson, R.S. Krausshar (eds.),
Proc. of *Function Theories in Higher Dimensions*,
Tampere 2006,
Advances in Applied Clifford Algebras, **17**(3), pp. 497-517 (2007).

**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.

**Mathematics Subject Classification (2000).** Primary 42A38; Secondary 11R52.

**Keywords.** Quaternions, Fourier transform, Clifford algebra, volume-time al-
gebra, spacetime algebra, automorphisms.

The original publication with DOI 10.1007/s00006-007-0037-8 is available at www.springerlink.com.

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