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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2410.09075 |
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Table of Contents:
- 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 $\mathfrak{a}^{*}_{\mathbb{C}}.$