Keywords
- Unitary Representation
- Linear Span
- Spherical Function
- Convolution Operator
- Homogeneous Tree
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
J.P. Arnaud, Fonctions sphériques et fonctions définies positive sur l'arbre homogène, C.R. Acad. Sc. Paris 290 (1980), 99–191.
R.A. Bonic, Symmetry in group algebras of discrete groups, Pacif. J. Math. 11 (1961), 73–94.
W. Betori, M. Pagliacci, Harmonic analysis for groups acting on trees, to appear in Boll. Un. Mat. It.
P. Cartier, Géomètrie et analyse sur les arbres, Lecture Notes in Math. 317, Springer-Verlag, Berlin, 1973, 123–140.
P. Cartier, Fonctions harmoniques sur un arbre, Symp. Math. 9 (1972), 203–270.
P. Cartier, Harmonic analysis on trees, Proc. Symp. Pure Math. Amer. Math. Soc. 26 (1972), 419–424.
J. Dixmier, Formes linéaires sur un anneau d'operateurs, Bull. Soc. Math. France 81 (1953), 9–39.
J. Dixmier, "Les C*-algèbres et leurs représentations", Gauthier-Villars, Paris, 1969.
J.L. Dunau, Etude d'une classe de marches aléatoires sur l'arbre homogène, Public. Laboratoire de Statistique et Probabilités, Université Paul Sabatier, Toulouse, 1976.
E.B. Dynkin, M.B. Maliutov, Random walks on groups with a finite number of generators, Soviet Math. (Doklady) 2 (1961), 399–402.
J. Duncan, J.H. Williamson, Spectra of elements in the measure algebra of a free group, Proc. Royal Irish Acad. 82 (1982), 109–120.
A. Figà-Talamanca, M.A. Picardello, Spherical functions and harmonic analysis on free groups, J. Functional Anal. 47 (1982), 281–304.
A. Figà-Talamanca, M.A. Picardello, "Harmonic analysis on free groups", Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, New York (in print).
P. Gerl, A local central limit theorem on some groups, Lecture Notes in Stat., Springer-Verlag, Berlin, 1981, 73–82.
A. Iozzi, M.A. Picardello, Graphs and convolution operators, to appear in "Topics in Modern Harmonic Analysis", Indam, Roma.
A.M. Mantero, A. Zappa, The Poisson transform and uniformly bounded representations of free groups, preprint.
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.
G. Warner, "Harmonic analysis on semisimple Lie groups", I and II, Springer-Verlag, Berlin, 1972.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Springer-Verlag
About this paper
Cite this paper
Iozzi, A., Picardello, M.A. (1983). Spherical functions on symmetric graphs. In: Mauceri, G., Ricci, F., Weiss, G. (eds) Harmonic Analysis. Lecture Notes in Mathematics, vol 992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0069168
Download citation
DOI: https://doi.org/10.1007/BFb0069168
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-12299-9
Online ISBN: 978-3-540-39885-1
eBook Packages: Springer Book Archive
