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1991 | 100 | 3 | 237-250
Tytuł artykułu

Spherical functions and uniformly bounded representations of free groups

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We give a construction of an analytic series of uniformly bounded representations of a free group G, through the action of G on its Poisson boundary. These representations are irreducible and give as their coefficients all the spherical functions on G which tend to zero at infinity. The principal and the complementary series of unitary representations are included. We also prove that this construction and the other known constructions lead to equivalent representations.
Czasopismo
Rocznik
Tom
100
Numer
3
Strony
237-250
Opis fizyczny
Daty
wydano
1991
otrzymano
1991-01-10
Twórcy
  • Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland
Bibliografia
  • [1] P. Cartier, Géométrie et analyse sur les arbres, Séminaire Bourbaki 24 (1971/72), Exposé 407.
  • [2] P. Cartier, Harmonic analysis on trees, in: Proc. Sympos. Pure Math. 26 (1972), 419-424.
  • [3] A. Figà-Talamanca and A. M. Picardello, Spherical functions and harmonic analysis on free groups, J. Funct. Anal. 47 (1982), 281-304.
  • [4] A. Figà-Talamanca and A. M. Picardello, Harmonic Analysis on Free Groups, M. Dekker, New York 1983.
  • [5] A. M. Mantero, T. Pytlik, R. Szwarc and A. Zappa, Equivalence of two series of spherical representations of a free group, Ann. Mat. Pura Appl., to appear.
  • [6] A. M. Mantero and A. Zappa, The Poisson transform and representations of a free group, J. Funct. Anal. 51 (1983), 372-399.
  • [7] A. M. Mantero and A. Zappa, Irreducibility of the analytic continuation of the principal series of a free group, J. Austral. Math. Soc. 43 (1987), 199-210.
  • [8] M. Pimsner, Cocycles on trees, J. Operator Theory 17 (1987), 121-128.
  • [9] T. Pytlik, Radial functions on free groups and a decomposition of the regular representation into irreducible components, J. Reine Angew. Math. 326 (1981), 124-135.
  • [10] T. Pytlik, Spherical functions and uniformly bounded representations of free groups, preprint 60 (1986), Math. Inst. Univ. Wrocław.
  • [11] T. Pytlik and R. Szwarc, An analytic family of uniformly bounded representations of free groups, Acta Math. 157 (1986), 287-309.
  • [12] S. Sawyer, Isotropic random walks in a tree, Z. Wahrsch. Verw. Gebiete 12 (1978), 279-292.
  • [13] R. Szwarc, An analytic series of irreducible representations of the free group, Ann. Inst. Fourier (Grenoble) 38 (1) (1988), 87-110.
  • [14] A. Valette, Cocycles d'arbres et représentations uniformément bornées, C. R. Acad. Sci. Paris 310 (1990), 703-708.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv100i3p237bwm
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