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Funktsional'nyi Analiz i ego Prilozheniya, 2009, Volume 43, Issue 1, Pages 37–54
DOI: https://doi.org/10.4213/faa2943 (Mi faa2943) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Horospherical Transform on Real Symmetric Varieties: Kernel and Cokernel

B. Krötz

Max-Planck-Institut für Mathematik
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DOI: https://doi.org/10.4213/faa2943
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.
Received: 14.05.2007
English version:
Functional Analysis and Its Applications, 2009, Volume 43, Issue 1, Pages 30–43
DOI: https://doi.org/10.1007/s10688-009-0004-3
Bibliographic databases:
Document Type: Article
UDC: 517.988.28
Language: Russian
Citation: B. Krötz, “Horospherical Transform on Real Symmetric Varieties: Kernel and Cokernel”, Funktsional. Anal. i Prilozhen., 43:1 (2009), 37–54; Funct. Anal. Appl., 43:1 (2009), 30–43
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
     
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