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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2409.09036 |
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| _version_ | 1866910603366367232 |
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| author | Oyadare, Olufemi O. |
| author_facet | Oyadare, Olufemi O. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_09036 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Paley-Wiener theorem for the Joint-Eigenspace Fourier transform on noncompact symmetric spaces Oyadare, Olufemi O. Functional Analysis 53C35, 43A90, 42A38 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. |
| title | Paley-Wiener theorem for the Joint-Eigenspace Fourier transform on noncompact symmetric spaces |
| topic | Functional Analysis 53C35, 43A90, 42A38 |
| url | https://arxiv.org/abs/2409.09036 |