A note on the $L^{2}-$harmonic analysis of the Joint-Eigenspace Fourier transform
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912069790466048 |
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| author | Oyadare, O. O. |
| author_facet | Oyadare, O. O. |
| 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 $\mathfrak{a}^{*}_{\mathbb{C}}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09075 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on the $L^{2}-$harmonic analysis of the Joint-Eigenspace Fourier transform Oyadare, O. O. Functional Analysis 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 $\mathfrak{a}^{*}_{\mathbb{C}}.$ |
| title | A note on the $L^{2}-$harmonic analysis of the Joint-Eigenspace Fourier transform |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2410.09075 |