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Furstenberg, H.

Translation-invariant cones of functions on semi-simple Lie groups. (English) Zbl 0178.16901

Bull. Am. Math. Soc. 71, 271-326 (1965).
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Cited in 2 Reviews
Cited in 26 Documents

Keywords:

functional analysis
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References:

[1] François Bruhat, Sur les représentations induites des groupes de Lie, Bull. Soc. Math. France 84 (1956), 97 – 205 (French). · Zbl 0074.10303
[2] Gustave Choquet, Le théorème de représentation intégrale dans les ensembles convexes compacts, Ann. Inst. Fourier Grenoble 10 (1960), 333 – 344 (French). · Zbl 0096.08201
[3] G. Choquet et J. Deny, Sur l’équation de convolution \mu = \mu * \sigma , C. R. Acad. Sci. Paris 250 (1960), 799-801. · Zbl 0093.12802
[4] N. Dunford and J. T. Schwartz, Linear operators, Interscience, New York, 1958.
[5] E. B. Dynkin, Non-negative eigenfunctions of the Laplace-Beltrami operator and Brownian motion in certain symmetric spaces, Dokl. Akad. Nauk SSSR 141 (1961), 288 – 291 (Russian). · Zbl 0116.36106
[6] Harry Furstenberg, A Poisson formula for semi-simple Lie groups, Ann. of Math. (2) 77 (1963), 335 – 386. · Zbl 0192.12704 · doi:10.2307/1970220
[7] I. M. Gel\(^{\prime}\)fand, Spherical functions in symmetric Riemann spaces, Doklady Akad. Nauk SSSR (N.S.) 70 (1950), 5 – 8 (Russian).
[8] SigurÄ’ur Helgason, Differential geometry and symmetric spaces, Pure and Applied Mathematics, Vol. XII, Academic Press, New York-London, 1962.
[9] L. H. Loomis, Unique direct integral decompositions on convex sets, Amer. J. Math. 84 (1962), 509 – 526. · Zbl 0124.32101 · doi:10.2307/2372987
[10] Calvin C. Moore, Compactifications of symmetric spaces, Amer. J. Math. 86 (1964), 201 – 218. · Zbl 0156.03202 · doi:10.2307/2373040
[11] Séminaire Sophus Lie, Théorie des algèbres de Lie, École Normale Supérieure 1954/1955.
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