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Spherical functions and harmonic analysis on free groups. (English) Zbl 0489.43008


MSC:

43A65 Representations of groups, semigroups, etc. (aspects of abstract harmonic analysis)
43A90 Harmonic analysis and spherical functions
22D10 Unitary representations of locally compact groups
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[1] Akemann, C; Ostrand, P, Computing norms in group C∗-algebras, Amer. J. math., 98, 1015-1047, (1976) · Zbl 0342.22008
[2] Bozejko, M, On λ(p) sets with minimal constant in discrete noncommutative groups, (), 407-412 · Zbl 0321.43004
[3] Cartier, P, Géométrie et analyse sur LES arbres, (), exposé 407 · Zbl 0267.14010
[4] Cartier, P, Harmonic analysis on trees, (), 419-424 · Zbl 0309.22009
[5] {\scJ. Cohen}, Operator norms on free groups, Boll. Un. Mat. Ital., in press. · Zbl 0518.46050
[6] {\scJ. Cohen and L. De Michele}, Radial Fourier-Stieltjes algebra of free groups, in “Operator Algebras and K-Theory,” Amer. Math. Soc. Contemporary Mathematical Series, Amer. Math. Soc., Providence, R. I., in press.
[7] Cowling, M, The kunze-Stein phenomenon, Ann. of math., 107, 209-234, (1978) · Zbl 0363.22007
[8] De Michele, L; Figà-Talamanca, A, Positive definite functions on free groups, Amer. J. math., 102, 503-509, (1980) · Zbl 0455.43003
[9] Dunau, J.L, Étude d’une classe de marches aléatoires sur l’arbre homogène, (1976), Publications du laboratoire de statistique, Université Paul Sabatier Toulouse
[10] Dynkin, E.B; Maliutov, M.B, Random walks on groups with a finite number of generators, Soviet math. dokl., 2, 399-402, (1961) · Zbl 0214.44101
[11] Eymard, P, L’algèbre de Fourier d’un groupe localement compact, Bull. soc. math. France, 92, 181-236, (1964) · Zbl 0169.46403
[12] Eymard, P, Le noyau de Poisson et la théorie des groupes, (), 107-132
[13] Furstenberg, H, Random walks and discrete subgroups of Lie groups, (), 1-63 · Zbl 0146.28502
[14] Gulizia, C.L, Harmonic analysis of SL(2) over a locally compact field, J. funct. anal., 12, 384-400, (1973) · Zbl 0253.43011
[15] Haagerup, U, An example of a non-nuclear C∗-algebra which has the metric approximation property, Invent. math., 50, 279-293, (1979) · Zbl 0408.46046
[16] Helgason, S, Eigenspaces of the Laplacian; integral representations and irreducibility, J. funct. anal., 17, 328-353, (1974) · Zbl 0303.43021
[17] Herz, C, Sur le phénomène de kunze-Stein, C.R. acad. sci. Paris ser. A, 271, 491-493, (1970) · Zbl 0198.18202
[18] Kesten, H, Symmetric random walks on groups, Trans. amer. math. soc., 92, 336-354, (1959) · Zbl 0092.33503
[19] Kunze, R.A; Stein, E.M, Uniformly bounded representations and harmonic analysis of the 2 × 2 unimodular group, Amer. J. math., 82, 1-62, (1960) · Zbl 0156.37104
[20] Leinert, M, Faltungsoperatoren auf gewissen discreten gruppen, Studia math., 12, 149-158, (1974) · Zbl 0262.43009
[21] Pytlik, T, Radial functions on free groups and a decomposition of the regular representation into irreducible components, J. reine angew. math., 326, 124-135, (1981) · Zbl 0464.22004
[22] Satake, I, Theory of spherical functions on reductive algebraic groups over p-adic fields, Publ. math. I.H.E.S., 18, 1-69, (1963)
[23] Sawyer, S, Isotropic random walks in a tree, Z. wahrsch., 12, 279-292, (1978) · Zbl 0362.60075
[24] Serre, J.P, Arbres, amalgames, SL2, Asterisque, 46, (1977)
[25] Warner, G, ()
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