Harmonic Analysis and Representation Theory for Groups Acting on Homogenous Tre…
Harmonic Analysis and Representation Theory for Groups Acting on Homogenous TreesAuthor(s): Alessandro Fig-Talamanca, Claudio Nebbia\nFormat: Paperback\nPublisher: Cambridge University Press, United Kingdom\nImprint: Cambridge University Press\nISBN-13: 9780521424448, 978-0521424448\nSynopsis\nThese 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 [url] 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 repres.
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