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Harmonic Analysis on Reductive Symmetric Spaces

  • Conference paper
European Congress of Mathematics

Part of the book series: Progress in Mathematics ((PM,volume 201))

Abstract

We give a relatively non-technical survey of some recent advances in the Fourier theory for semisimple symmetric spaces. There are three major results: An inversion formula for the Fourier transform, a Paley—Wiener theorem, which describes the Fourier image of the space of compactly supported smooth functions, and the Plancherel theorem, which describes the decomposition into irreducibles of the regular representation.

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Utrecht, P.O. Box 80010, NL-3508 TA, Utrecht, The Netherlands

    Erik van den Ban

  2. Department of Mathematics, University of Copenhagen, Universitetsparken 5, DK-2100, Copenhagen Ø, Denmark

    Henrik Schlichtkrull

Authors
  1. Erik van den Ban
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  2. Henrik Schlichtkrull
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Editor information

Editors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Carles Casacuberta  & Joan Verdera  & 

  2. Departament d’Algebra i Geometria Facultat de Matemàtiques, Universitat de Barcelona, 08007, Barcelona, Spain

    Rosa Maria Miró-Roig

  3. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, 08028, Barcelona, Spain

    Sebastià Xambó-Descamps

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© 2001 Springer Basel AG

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van den Ban, E., Schlichtkrull, H. (2001). Harmonic Analysis on Reductive Symmetric Spaces. In: Casacuberta, C., Miró-Roig, R.M., Verdera, J., Xambó-Descamps, S. (eds) European Congress of Mathematics. Progress in Mathematics, vol 201. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8268-2_35

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  • DOI: https://doi.org/10.1007/978-3-0348-8268-2_35

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9497-5

  • Online ISBN: 978-3-0348-8268-2

  • eBook Packages: Springer Book Archive

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