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
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
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