In the research paper "Octonion Fourier Transform(OFT) of real-valued functions of three variables selected properties and examples" written by Łukasz Błaszczyka and Kajetana M. Snopek, they have taken UOFT (f) = ∫ R3 u (x)e^{-e12πf1x1} e^{-e22πf2x2}e^{-e42πf3x3} dx. Generally, octonions have 1, e1,e2,....,e7 as basic octonions. But in the definition of octonion Fourier transform they have taken three of them for the 3-dimensional case. It's all right.
Ques: Why have they taken e1,e2,e4 into consideration in the definition of OFT? Why they have not considered e1,e2,e3 or e1,e2,e5 or any other possible combinations? If all are possible them there will be 210 such definitions of OFT out of which some may be similar.
Dear Awniya Kumar
Because it has to be done in this way otherwise it cause undesirable outcome.
Kind Regards
Qamar Ul Islam
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