What is the Joint-Eigenspace transform on a symmetric space of non-compact type and how does it subsumes the Helgason Fourier transform??

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Olufemi O. Oyadare

The Poisson transform image of the Helgason Fourier transform provides a method of completion.

Ruhi Sharmin

The Joint-Eigenspace transform on a symmetric space of non-compact type generalizes the Helgason Fourier transform by incorporating multiple eigenspaces simultaneously. The Poisson transform image of the Helgason Fourier transform provides a method for completion within this broader framework. Does that answer your question? Thanks.