E. Hitzer
OPS-QFTs: A new type of quaternion Fourier transforms based on the orthogonal planes split with one or two general pure quaternions
Numerical Analysis and Applied Mathematics ICNAAM 2011, AIP Conf. Proc. 1389, pp. 280--283 (2011), doi: 10.1063/1.3636721

Abstract: We explain the orthogonal planes split (OPS) of quaternions based on the arbitrary choice of one or two linearly independent pure unit quaternions f,g. Next we systematically generalize the quaternionic Fourier transform (QFT) applied to quaternion fields to conform with the OPS determined by f,g, or by only one pure unit quaternion f, comment on their geometric meaning, and establish inverse transformations.

Keywords: Clifford geometric algebra, quaternion geometry, quaternion Fourier transform, inverse Fourier transform, orthogonal planes split.

AMS Subject Classification: 15A66, 42A38

[PDF] 977 kb

[Geometric Calculus Japan index]