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 ...
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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.
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Add this copy of Lms: 162 Harmonic Analysis Theory (London Mathematical to cart. $80.33, good condition, Sold by Bonita rated 4.0 out of 5 stars, ships from Hialeah, FL, UNITED STATES, published 2008 by Cambridge University Press.
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New. C. Trade paperback (US). 164 p. London Mathematical Society Lecture Note Series . Worked examples or Exercises. Intended for professional and scholarly audience.
