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A note on the $L^{2}-$harmonic analysis of the Joint-Eigenspace Fourier transform (2410.09075v1)
Published 3 Oct 2024 in math.FA
Abstract: We consider the irreducibility of the regular representation of a noncompact semisimpe Lie group $G$ on the Hilbert space of the image of the Joint-Eigenspace Fourier transform on its corresponding symmetric space $G/K.$ The $L{2}-$decomposition of the Joint-Eigenspace Fourier transform leads to the complete characterization of the said irreducibility in terms of the simplicity of a pair of members of $\mathfrak{a}{*}_{\mathbb{C}}.$