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The Fourier transform on symmetric spaces. (English) Zbl 0611.43005
Élie Cartan et les mathématiques d’aujourd’hui, The mathematical heritage of Elie Cartan, Semin. Lyon 1984, Astérisque, No.Hors Sér. 1985, 151-164 (1985).
[For the entire collection see Zbl 0573.00010.]
This is a short survey reviewing first the Fourier transform on a Riemannian symmetric space G/K of non-compact type, then on a compact symmetric space U/K. For dual symmetric spaces G/K and U/K the author asks whether inversion formulas for G/K and U/K are analytic continuation of each other. At last some results concerning semisimple symmetric spaces are briefly described.
Reviewer: J.Faraut

43A85 Harmonic analysis on homogeneous spaces
53C35 Differential geometry of symmetric spaces