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Funktsional. Anal. i Prilozhen., 2008, Volume 42, Issue 4, Pages 50–59 (Mi faa2931)  

This article is cited in 4 scientific papers (total in 4 papers)

Horospherical Transform on Riemannian Symmetric Manifolds of Noncompact Type

S. G. Gindikin

Rutgers, The State University of New Jersey, Department of Mathematics

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

DOI: https://doi.org/10.4213/faa2931

Full text: PDF file (190 kB)
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English version:
Functional Analysis and Its Applications, 2008, 42:4, 290–297

Bibliographic databases:

UDC: 517.988.28
Received: 23.07.2008

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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\paper Horospherical Transform on Riemannian Symmetric Manifolds of Noncompact Type
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gindikin S., Goodman R., “Restricted Roots and Restricted Form of the Weyl Dimension Formula for Spherical Varieties”, J. Lie Theory, 23:1 (2013), 257–311  mathscinet  zmath  isi  elib
    2. Simon Gindikin, “Local inversion formulas for horospherical transforms”, Mosc. Math. J., 13:2 (2013), 267–280  mathnet  crossref  mathscinet
    3. Rubin B., “New Inversion Formulas for the Horospherical Transform”, J. Geom. Anal., 27:1 (2017), 908–946  crossref  mathscinet  zmath  isi  scopus
    4. Bray W.O., Rubin B., “Radon Transforms Over Lower-Dimensional Horospheres in Real Hyperbolic Space”, Trans. Am. Math. Soc., 372:2 (2019), 1091–1112  crossref  isi
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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