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Spherical functions on a \(p\)-adic Chevalley group. (English) Zbl 0273.22012

MSC:
22E35 Analysis on \(p\)-adic Lie groups
11R56 Adèle rings and groups
42A85 Convolution, factorization for one variable harmonic analysis
43A25 Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups
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[1] François Bruhat, Sur une classe du sous-groupes compacts maximaux des groupes de Chevalley sur un corps \?-adique, Inst. Hautes Études Sci. Publ. Math. 23 (1964), 45 – 74 (French). · Zbl 0228.20014
[2] R. Godement, Introduction aux travaux de A. Selberg, Sém, Bourbaki 9 (1956-1957). · Zbl 0202.40902
[3] SigurÄ’ur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962.
[4] N. Iwahori and H. Matsumoto, On some Bruhat decomposition and the structure of the Hecke rings of \?-adic Chevalley groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 5 – 48. · Zbl 0228.20015
[5] F. I. Mautner, Spherical functions over \?-adic fields. I, Amer. J. Math. 80 (1958), 441 – 457. · Zbl 0092.12501
[6] Ichirô Satake, Theory of spherical functions on reductive algebraic groups over \?-adic fields, Inst. Hautes Études Sci. Publ. Math. 18 (1963), 5 – 69. · Zbl 0122.28501
[7] Tsuneo Tamagawa, On Selberg’s trace formula, J. Fac. Sci. Univ. Tokyo Sect. I 8 (1960), 363 – 386. · Zbl 0118.11405
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