This article is cited in 3 papers

Horospherical Transform on Real Symmetric Varieties: Kernel and Cokernel

B. Krötz

Max-Planck-Institut für Mathematik

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 $\Xi$ of horospheres to $Y$. The horospherical transform relates certain integrable analytic functions on $Y$ to analytic functions on $\Xi$ 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 $Y$.

Keywords: semisimple symmetric space, horospherical transform, Fourier transform, Plancherel theorem.

UDC: 517.988.28

Received: 14.05.2007

DOI: 10.4213/faa2943

 English version: Functional Analysis and Its Applications, 2009, 43:1, 30–43

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