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arXiv · 2410.09075

A note on the $L^{2}-$harmonic analysis of the Joint-Eigenspace Fourier transform

O. O. Oyadare
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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 $\mathfrak{a}^{*}_{\mathbb{C}}.$

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O. O. Oyadare. 2024-10-03. A note on the $L^{2}-$harmonic analysis of the Joint-Eigenspace Fourier transform. https://arxiv.org/abs/2410.09075

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