Pacific Journal of Mathematics

Groups of isometries of a tree and the Kunze-Stein phenomenon.

Claudio Nebbia

Article information

Source
Pacific J. Math., Volume 133, Number 1 (1988), 141-149.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102689572

Mathematical Reviews number (MathSciNet)
MR936361

Zentralblatt MATH identifier
0646.43006

Subjects
Primary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc.
Secondary: 43A85: Analysis on homogeneous spaces

Citation

Nebbia, Claudio. Groups of isometries of a tree and the Kunze-Stein phenomenon. Pacific J. Math. 133 (1988), no. 1, 141--149. https://projecteuclid.org/euclid.pjm/1102689572


Export citation

References

  • [I] W. Betori and M. Pagliacci, Harmonic analysisfor groups acting on trees, Boll. Un. Mat. It., 3-B (1984), 333-349.
  • [2] F. Bouaziz-Kellil, Representations spheriquesdes groupesagissant transitivement sur un arbre semi homogene, These de 3-eme cycle, Universite de Nancy I.
  • [3] P. Cartier, Functions harmoniques sur un arbre, Symp. Math., 9 (1972), 203- 270.
  • [4] F. Choucroun, Groupes operant simplement transitivement sur un arbre ho- mogene et plongements dans PGL2(), C. R. Acad. Sci. Paris, 298 (1984), 313- 315.
  • [5] J. M. Cohen and L. deMichele, Radial Fourier-Stieltjesalgebra on free groups, Contemporary Math., 10 (Operator algebras and A^-theory), 1982.
  • [6] M. Cowling, The Kunze-Stein phenomenon, Ann. of Math., 107 (1978), 209- 234.
  • [7] P. Eymard, L'algebre de Fourier d'un groupe localment compact, Bull. Soc. Math. France, 92 (1964), 181-236.
  • [8] P. Eymard et N. Lohoue, Sur la racine carree du noyau de Poisson dans les espaces symetriques et une conjecture de E. M. Stein, Ann. Sci. Ecole Norm. Sup., Ser4 (8) n. 2 (1975).
  • [9] J. Faraut, Analyse harmonique sur les paires de Gelfand et les espaces hyper- boliques,Analyse harmonique Nancy 1980, CIMPA, Nice (1983).
  • [10] J. Faraut and M. A. Picardello, The Plancherel measure for symmetric graphs, Ann di Mat. Pura Appl, (IV) 138 (1984), 151-155.
  • [II] A. Figa-Talamanca and M. A. Picardello, Sphericalfunctions and harmonic anal- ysis on free groups,J. Funct. Anal., 47 (1982), 281-304.
  • [12] A. Figa-Talamanca and M. A. Picardello, Harmonic Analysis on Free Groups,Lecture notes in pure and applied mathematics, Marcel Dekker, New York, 1983.
  • [13] C. L. Gulizia, Harmonic analysis o/SL(2) over a locally compact field, J. Funct. Anal., 12(1973), 384-400.
  • [14] C. Herz, Sur le phenomene de Kunze-Stein, C. R. Acad. Sci. Paris, 271 (1970), 491-493.
  • [15] R. A. Kunze and E. M. Stein, Uniformly bounded representationsand harmonic analysis of the 2 x 2 real unimodular group, Amer. J. Math., 82 (1960), 1-62.
  • [16] S. Lang, SL2(R), Addison-Wesley, Reading, Mass. 1975.
  • [17] J. P. Serre, Arbres, amalgames, SL2, Asterisque, 46 (1977).
  • [18] J. Tits, Sur le groupe des automorphismes d'un arbre, Essays on topology and related topics, Memoires dedies a G. de Rham, Springer-Verlag, (1970), 188- 211.