$L^r$- Schwartz spaces on split rank one semisimple symmetric spaces
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909009945034752 |
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| author | Pusti, Sanjoy Sitiraju, Iswarya |
| author_facet | Pusti, Sanjoy Sitiraju, Iswarya |
| contents | We study the left $K$-invariant $L^r$-Schwartz space and its Fourier transform on split rank one semisimple symmetric spaces $G/H$ for $0<r\leq 2$. We explicitly determine the kernel of the Fourier transform and show that it is spanned by eigenfunctions associated with the discrete spectrum of the Laplace--Beltrami operator on $G/H$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_01252 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | $L^r$- Schwartz spaces on split rank one semisimple symmetric spaces Pusti, Sanjoy Sitiraju, Iswarya Functional Analysis 43A85, 43A90, 33C67, 22E30 We study the left $K$-invariant $L^r$-Schwartz space and its Fourier transform on split rank one semisimple symmetric spaces $G/H$ for $0<r\leq 2$. We explicitly determine the kernel of the Fourier transform and show that it is spanned by eigenfunctions associated with the discrete spectrum of the Laplace--Beltrami operator on $G/H$. |
| title | $L^r$- Schwartz spaces on split rank one semisimple symmetric spaces |
| topic | Functional Analysis 43A85, 43A90, 33C67, 22E30 |
| url | https://arxiv.org/abs/2605.01252 |