Horospherical transform on real symmetric varieties: Kernel and cokernel |
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Authors: | Bernhard Krötz |
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Affiliation: | (1) Max-Planck-Institut für Mathematik, Bonn, Germany |
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Abstract: | In this paper, we define a horospherical transform for a semisimple symmetric space Y. A natural double fibration is used to assign a more geometrical space Ξ of horospheres to Y. The horospherical transform relates certain integrable analytic functions on Y to analytic functions on Ξ by fiber integration. We determine the kernel of the horospherical transform and establish that the transform is injective on functions belonging to the most continuous spectrum of Y. |
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Keywords: | semisimple symmetric space horospherical transform Fourier transform Plancherel theorem. |
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