The JEFT is the Poisson transform of the Helgason Fourier transform, making it a joint eigenfunction of every invariant differential operator on the symmetric space.
What is the JEFT?
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The JEFT is the acronym for the Joint-Eigenspace Fourier Transform defined on a noncompact symmetric space. It is a consequence of a general construction of a Fourier transform modelled on the Harish-Chandra Fourier transform (on a semi-simple Lie group with finite centre) which (on the corresponding symmetric space of the noncompact type) serves as the Poisson-completion of the famous Helgason Fourier transform
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What is the JEFT?
The JEFT is the Poisson transform of the Helgason Fourier transform, making it a joint eigenfunction of every invariant differential operator on the symmetric space.