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arXiv · 2409.09036

Paley-Wiener theorem for the Joint-Eigenspace Fourier transform on noncompact symmetric spaces

Olufemi O. Oyadare
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Abstract

This paper conducts a geometric analysis of the Joint-Eigenspace Fourier transform of the symmetric space of the non-compact type. Our study shows how the Poisson transform builds up the well-known Helgason Fourier transform for an analysis of the complete duality of the underlying symetric space. Among other results, we establish an inversion formula, a Plancherel formula and (as our main result) a Paley-Wiener theorem for the Joint-Eigenspace Fourier transform on any noncompact symmetric space.

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Olufemi O. Oyadare. 2024-08-20. Paley-Wiener theorem for the Joint-Eigenspace Fourier transform on noncompact symmetric spaces. https://arxiv.org/abs/2409.09036

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