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arXiv · 2605.01252

$L^r$- Schwartz spaces on split rank one semisimple symmetric spaces

Sanjoy Pusti·Iswarya Sitiraju
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Abstract

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 $G/H$.

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Sanjoy Pusti, Iswarya Sitiraju. 2026-05-02. $L^r$- Schwartz spaces on split rank one semisimple symmetric spaces. https://arxiv.org/abs/2605.01252

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