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Funktsional'nyi Analiz i ego Prilozheniya, 2008, Volume 42, Issue 4, Pages 50–59
DOI: https://doi.org/10.4213/faa2931 (Mi faa2931) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Horospherical Transform on Riemannian Symmetric Manifolds of Noncompact Type

S. G. Gindikin

Rutgers, The State University of New Jersey, Department of Mathematics
Full-text PDF (190 kB) Citations (6)
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DOI: https://doi.org/10.4213/faa2931
Abstract: We discuss I. M. Gelfand's project of rebuilding the representation theory of semisimple Lie groups on the basis of integral geometry. The basic examples are related to harmonic analysis and the horospherical transform on symmetric manifolds. Specifically, we consider the inversion of this transform on Riemannian symmetric manifolds of noncompact type. In the known explicit inversion formulas, the nonlocal part essentially depends on the type of the root system. We suggest a universal modification of this operator.
Keywords: symmetric manifold, horospherical transform, inversion formula, Plancherel formula.
Received: 23.07.2008
English version:
Functional Analysis and Its Applications, 2008, Volume 42, Issue 4, Pages 290–297
DOI: https://doi.org/10.1007/s10688-008-0042-2
Bibliographic databases:
Document Type: Article
UDC: 517.988.28
Language: Russian
Citation: S. G. Gindikin, “Horospherical Transform on Riemannian Symmetric Manifolds of Noncompact Type”, Funktsional. Anal. i Prilozhen., 42:4 (2008), 50–59; Funct. Anal. Appl., 42:4 (2008), 290–297
Citation in format AMSBIB
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    • This publication is cited in the following 6 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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