Harmonic Analysis and Representation Theory for Groups Acting on Homogenous Trees

These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree.

Alessandro Figá-Talamanca (Author), Claudio Nebbia (Author)

9780521424448, Cambridge University Press

Paperback, published 28 June 1991

164 pages
22.8 x 15.2 x 1 cm, 0.25 kg

These notes treat in full detail the theory of representations of the group of automorphisms of a homogeneous tree. The unitary irreducible representations are classified in three types: a continuous series of spherical representations; two special representations; and a countable series of cuspidal representations as defined by G.I. Ol'shiankii. Several notable subgroups of the full automorphism group are also considered. The theory of spherical functions as eigenvalues of a Laplace (or Hecke) operator on the tree is used to introduce spherical representations and their restrictions to discrete subgroups. This will be an excellent companion for all researchers into harmonic analysis or representation theory.

Chapter 1
Chapter 2
Chapter 3
Appendix

Subject Areas: Probability & statistics [PBT]