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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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
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