The kernel of the Fourier transform on the left K-invariant L^r-Schwartz space for split rank one semisimple symmetric spaces is spanned by eigenfunctions associated with the discrete spectrum of the Laplace-Beltrami operator.
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$L^r$- Schwartz spaces on split rank one semisimple symmetric spaces
The kernel of the Fourier transform on the left K-invariant L^r-Schwartz space for split rank one semisimple symmetric spaces is spanned by eigenfunctions associated with the discrete spectrum of the Laplace-Beltrami operator.