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

2024/08/20 by Oyadare, Olufemi O.
#42A38 #43A90 #53C35 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2409.09036

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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